FRANKLIN  INSTITUTE  LIBRARY 

PHILADELPHIA,  PA. 
Class.  <C?.9.3.        Book^S.b..2.7...  Accession... <o  .2*3-  

REFERENCE 


t      —  — j  —  — ~ 

observance  of  the  rules  of  the  Library,  and  for  the  valine  of  such  books  as 
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$  # 


Digitized  by 

the  Internet  Archive 

in  2015 

https://archive.org/details/operativemasonryOOshaw 


NEW  WORK  ON 


ARCHITECTURE. 

SECOND  EDITION  ENLARGED  AND  IMPROVED. 

Just  published,  by  MARSH,  CAPEN  AND  LYON,  362, 
Washington  Street,  Boston,  Civil  Architecture,  or  a  complete  the- 
oretical and  practical  system  of  Building — containing  the  funda- 
mental principles  of  the  Art,  with  the  five  Orders  of  Architecture. 
Also,  a  great  variety  of  examples  selected  from  Vitruvius,  Stuart, 
Chambers  and  Nicholson — with  many  useful  and  elegant  Orna- 
ments, and  rules  for  projecting  them.  By  Edward  Shaw,  Archi- 
tect. Illustrated  with  95  Copper-plate  Engravings,  printed  in  good 
style  and  on  fine  paper. 

RECOMMENDATIONS. 
Gentlemen — I  have  been  gratified  in  the  examination  of  Mr. 
Shaw's  Work  on  "Civil  Architecture,"  recently  published  by  you. 
Mr.  S.  seems  to  have  collected  his  examples  with  judgment  and 
taste,  and  also  with  a  good  knowledge  of  the  wants  of  the  country 
on  this  subject.  The  more  practical,  or  perhaps  I  should  say  ope- 
rative parts  of  the  work,  strike  me  as  being  peculiarly  useful ; 
especially  in  country  places,  where  the  Architect  is  not  at  hand  to  fur- 
nish designs  and  plans.  The  examples  from  Grecian  and  Roman 
authors  do  credit,  not  only  to  the  Collector,  but  to  those  who  exe- 
cuted the  plates.  I  hope  the  author  of  this  work  may  be  well  remu- 
nerated by  a  liberal  public,  and  that  the  publishers  may  not  lose 
their  reward.  Respectfully, 

Boston,  Aug.  1,  1831.  JOSEPH.  JENKINS. 

Extract  of  a  letter  from  Wm.  Austin^  Esq.    Warden  of  Mass.  State  Prison. 

"Dear  Sir: — Having  examined  your  late  work  on  "Civil  Archi- 
tecture" with  much  profit  and  pleasure,  I  feel  it  due  to  your  obvi- 
ous and  persevering  industry  and  deep  research  in  all  that  relates  to 
that  elegant  and  useful  art — to  olfer  my  feeble  testimony  in  favor  of 
your  very  elaborate  compilation  ;  of  the  general  arrangement  of  the 
subject,  and  more  especially  of  your  own  intelligible  explanations, 
historical  remarks  and  judicious  demonstrations. 

Very  respectfully,  your  obedient  servant, 
Charlestown,  Sept.  5,  1831.  WM.  AUSTIN. 

Sir — In  answer  to  yours  respecting  the  merits  of  your  Book  now 
published  on  Architecture,  I  do  with  confidence  recommend  it  to 
the  Public,  as  a  book  well  calculated  in  every  way  to  be  useful  for 
the  purpose  you  have  designed  it.         Yours  &c. 

Boston,  April  22,  1831.  C.  G.  HALL  Architect. 

Dear  Sir,— Having  carefully  examined  the  book  you  sent  us, 
entitled  "Civil  Architecture,"  we  find  it  such  a  work  as  should  be  in 
the  hands  of  every  practical  builder,  especially  in  country  towns. 
It  contains  numerous  Grecian  and  Roman  examples,  judiciously  se- 
lected from  the  best  authors,  embracing  in  a  cheap  volume  all 
that  is  of  material  service  to  practical  men,  from  numerous  and 
expensive  works  on  this  subject.  We  also  cheerfully  recommend  it 
to  the  attention  of  our  brother  mechanics  as  a  work  well  worthy  of 
their  patronage.  SALMON  WASHBURN. 

Boston,  May  10,  1831.  JEREMIAH  WASHBURN. 

'      y  THEODORE  WASHBURN. 

WILLIAM  WASHBURN. 

To  Edward  Shaw,  Esq, 


OPERATIVE  MASONRY: 

O  R  , 

A  THEORETICAL  AND  PRACTICAL 
TREATISE   OP  BUILDING; 

CONTAINING 

A     SCIENTIFIC     ACCOUNT     OF     STONES,    CLAYS,    BRICKS,  MORTARS, 
CEMENTS,  &C.;  A  DESCRIPTION  OF  THEIR  COMPONENT 
PARTS,  WITH  THE  MANNER  OF  PREPARING 
AND    USING  THEM. 

The  Fundamental  Rules  in  Geometry. 

O  N 

MASONRY  AND  STONE-CUTTING, 

WITH  THEIR  APPLICATION  TO  PRACTICE. 

»'     5"»    ?>  \  i        i  »   i       •  o  '  •  "     »     *        /  \    9    \     \    *,    *    »     •  , 

>       o-  ,  >•    >  *..'>  •»    »>>»»>  *i<    >»>  >  >'  »  •  >     •»>      '  .  «  J  » 

ILLUSTRATED    „1R TP,  „  KORT  t    .CGBPER-PL^TE  ENGRAVINGS. 


BY  EDWARD  SHAW,  ARCHITECT, 

Author  of  Civil  Architecture,  fyc. 


BOSTON: 
MARSH,  CAPEN  &  LYON. 
1832. 


Entered  according  to  Act  of  Congress  in  the  year  1832,  by 

Marsh,  Capen  &  Lyon. 
in  the  Clerk's  Office  of  the  District  Court  of  Massachusetts. 


PREFACE. 


In  preparing  this  work  for  the  public,  it  has  been  the  design  of  the  Compiler 
to  avoid  prolixity,  by  the  rejection  of  such  things  as  are  already  known  to 
the  mechanic,  and  to  furnish  him  with  a  knowledge  of  the  principles  and  facts, 
on  which  he  might  be  supposed  to  require  information. 

Most  works  on  this  subject,  set  out  with  a  description  of  all  the  minutiae  of  the 
art  of  building;  and  though  they  may,  perhaps,  exhibit  something  that  will  be 
useful  to  the  apprentice,  yet  they  contain  much  that  is  of  no  importance  to  the 
practical  mechanic;  while  the  price  is  so  much  enhanced,  that  few  can  well 
afford  to  possess  them. 

As  permanency  in  building  seems,  at  the  present  day,  to  be  an  object  more 
desirable  than  formerly,  it  has  been  thought  that  a  brief  account  of  the  nature 
and  qualities  of  building  materials,  with  a  short  exposition  of  their  component 
parts,  would  not  be  misplaced  in  a  treatise  of  this  kind.  The  Compiler  flatters 
himself,  that  he  has,  on  this  head,  furnished  some  information,  that  will  be 
serviceable  not  only  to  the  operator  but  to  the  proprietor ;  neither  of  whom,  can, 
with  safety,  remain  unacquainted  with  the  quality  of  the  materials  employed. 

The  best  writers,  on  the  various  subjects  treated  of  in  this  work,  have  been 
consulted,  and  such  use  made  of  their  labors,  by  abridging,  altering,  abstracting, 
and  condensing,  as  seemed  advisable  to  the  Compiler.  While  he  has  added 
much  that  has  been  the  result  of  many  years  of  practical  experience  and 
personal  observation. 

In  short,  brevity  with  perspicuity,  and  utility  with  cheapness,  have  been 
aimed  at :  how  far  they  have  been  attained,  is  submitted  to  the  decision  of  an 
enlightened  and  indulgent  public. 


633 


CONTENTS. 


CHAPTER  I. 

Section  1  Marble,        -  Page  7 

"       2  The  polishing  of  Marble,           -          -  "  13 

3  Artificial  Marble,     -  "  14 

«       4  The  coloring  of  Marble,            -          -  "  15 

5  Granite,        -----  "17 

6  Sienite,   "  25 

7  Green  Stone,            -          -          -          -  ♦<  27 
"       8  Sand  Stone  or  Free  Stone,       '  -          -  -  "27 

«       9  Gneiss,   "29 

"      10  Mica  Slate,   "  30 

"      11  Roof  Slate,             ...          -  "30 

"      12  Soap  Stone,   "32 

"      13  Gypsum,   "33 

"      14  Puzzolana,   "34 

«      15  Tras  or  Terrass,      -  "34 

"      16  Quarrying,       -          -          -          -  -         "  35 

Table  showing  the  weight  of  Stone,            -  "  40 

Rules  for  measuring  Stone,      -          -  "  41 

CHAPTER  IT. 

Section  1  Clay,           -          -          -          -          -  Page  45 

"       2  Brick  making,     -          -          -          -  "  46 

3  Pressed  Bricks,        -  "48 

4  The  use  of  Bricks  in  building,    -          -  -  "50 

5  Tiles,          -          .          -                    -  "  51 
"       6  Compact  Lime  Stone,    -          -          -  "  51 

7  Burning  of  Lime,      ...          -  "62 

"       8  Common  Mortar  and  Cement,     -          -  -        "  53 

9  Observations  on  Mortar,       -          -          -  "54 

10  Making  of  Mortar,         -                    -  "  54 

"      11  Monsieur  Loriat's  Mortar,     -          -          -  "55 

"      12  Dr.  Higginson  on  Mortar,          -          -  "  55 

"      13  Observations  on  antique  Mortar,       -          -  "58 

14  Stucco,             -          -          -          -  "  59 

"      15  Adam's  oil  Cement,            -          -          -  "60 


6 


CONTENTS. 


Section  1 
2 
3 
4 


Section  1 


9 

10 

<c 

11 

12 

<( 

13 
14 
15 


16 


Section  1 

«  2 

"  3 
<<  << 

4 

5 
6 


Page. 
62 
65 
69 
70 


CHAPTER  III. 
PRACTICAL  GEOMETRY. 

The  position  of  Lines  and  Points,  - 
Curved  Lines, 

Properties  of  Lines  and  Planes, 
The  right  section  of  Arches, 

CHAPTER  IV. 

Definition  of  Trehedrals,     -  -  -  72 

Oblique  Cylindroid,       -  -  -  74 

Projection  of  tangent  Lines  to  a  cylindrical 

surface,  -  -  -  76 

Application  of  Geometry  to  Planes,  &>c,  77 
The  developement  of  the  surfaces  of  Solids,  83 
Definitions  of  Masonry,  Walls,  Vaulting,  &c,  85 
Oblique  Arches,  -  87 

Oblique  Arches  for  Canals,  -  -  93 

Oblique  Arches  adapted  to  Bridges,  -  95 
The  formation  of  the  Intrados  to  oblique  Arches,  97 
Projected  curves  of  the  Intrados,  -  98 

Developement  of  the  Intrados,         -  -  99 

Circular  Arch  in  a  circular  Wall,  -  101 
Conic  Arch  in  a  cylindrical  Wall,  -  -  1C2 

The  construction  of  an  uniform  Arch  of  a 

Conical  Form,  -  103 
The  construction  of  moulds  for  a  spherical  Niche,  105 

106 
108 
108 
110 
117 
120 
122 
123 
123 


Example  of  Niches  with  radiating  Joints, 
An  Arch  with  splayed  Jambs, 
Example  of  Niches  in  a  straight  Wall,  - 
Spherical  Domes,  - 

Another  method  of  forming  spherical  Domes, 
The  construction  of  groined  Vaults, 
Of  raking  Mouldings,  - 
Construction  of  a  Lintel, 
Construction  of  an  Architrave, 
The  elevation  of  a  semicircular  arched  Door- 
way, -  124 
The  construction  of  Gothic  Vaults,  -  -  125 
The  formation  of  Stones  for  Vaults,  -  126 
Gothic  Ceilings,  -  -  -  -  126 
A  Gothic  Isosceles  Arch,         -          -  127 

CHAPTER  V. 

Of  Ancient  Walls,  -          -  -          -  129 

Ancient  wall  at  Naples,  &c,  -  130 

Construction  of  Brick  Arches,  -          -  131 

Brick  Laying,     -  131 

An  explanation  of  Bonds,    -  -          -  132 

Remarks  on  Brick-work,  -          -  134 

Foundations,          -  135 

Brick  Walls,     -          -  -  136 

The  construction  of  Chimnies,  -          -  138 

Chimney  Pieces,          -  -  189 


Plate. 
1 
2 
3 
4 


7 

8 

9.  10 
11 
12 
13 
14 
15 
16 
17 

18 

19.  20 

21.22 

23 
24 
25 
26 
27 
28 

29 
30 
31 
32 
33 


34 
35 
36 
37 
37 

36 
37 
39 
40 


CHAPTER  I. 


SECTION  I.  Marble. 

The  class  of  stones  denominated  Calcareous,  is  exceedingly  nu- 
merous and  abundant  in  nature.  Of  these,  marble  is  the  most  im- 
portant. It  is  a  granular  carbonate  of  lime,  or  a  compact  lime 
stone,  varying  in  color,  texture,  and  hardness.  Its  structure  is  both 
foliated  and  granular.  The  grains  are  of  various  sizes,  from  coarse 
to  very  fine,  sometimes,  indeed,  so  fine  that  the  mass  appears 
almost  compact.  When  these  grains  are  white,  and  of  a  moderate 
size,  this  mineral  strongly  resembles  white  sugar  in  solid  masses. 

Its  fracture  is  foliated  ;  but  the  faces  of  the  laminae,  which  vary 
in  extent,  according  to  the  size  of  the  grains,  are  sometimes  distin- 
guishable only  by  their  glimmering  lustre.  When  the  structure  is 
very  finely  granular,  the  fracture  often  becomes  a  little  splintery. 

Both  its  hardness,  and  the  cohesion  of  its  grains,  are  somewhat 
variable.  In  some  cases,  its  hardness  undoubtedly  depends  on  the 
presence  of  siliceous  particles  ;  indeed,  it  sometimes  gives  a  few 
sparks  with  steel.  Its  specific  gravity  usually  lies  between  2.  71, 
and  2.  84,  water  being  1 . — That  is,  water  as  a  standard  being  taken 
as  an  unit,  the  specific  gravity  of  marble  is  from  2  71-100  units  to 
2  84-100  units  when  compared  to  water,  or  about -2  3-4  times  greater. 

It  is  more  or  less  translucent,  but,  in  the  dark  colored  varieties, 
at  the  edges  only.  Its  color  is  most  commonly  white  or  gray,  often 
snow  white,  and  sometimes  grayish  black.  It  also  presents  certain 
shades  of  blue,  green,  red,  or  yellow.  Most  frequently  the  colors 
are  uniform,  but  sometimes  variegated  in  spots,  veins,  or  clouds, 
arising  from  the  intermixture  of  foreign  substances. 

Marble  is  essentially  a  carbonate  of  lime,  which  is  composed  of  57 
parts  of  lime,  and  43  parts  of  carbonic  acid  ;  a  little  water  is  usually 
present.  It  is  soluble  in  nitric  acid  ;  and  by  the  escape  of  carbonic 
acid,  more  or  less  effervesence  is  produced ;  some  varieties,  how- 
ever, effervesce  very  slowly.  Before  the  blowpipe  it  decrepitates, 
and,  if  pure  carbonate  of  lime,  it  is  perfectly  infusible  ;  but,  by  a 
strong  heat,  its  carbonic  acid  is  driven  off,  and  quick-lime  or  pure 
lime,  whose  taste  is  well  known,  remains. 

Marble^  in  the  strict  propriety  of  the  term,  should  be  confined  to 
those  varieties  of  carbonate  of  lime,  which  are  susceptible  of  a 
polish  ;  including  also  some  minerals,  in  which  carbonate  of  lime 
abounds.  But  among  artists  this  term  is  sometimes  extended  to 
serpentine,  basalt,  &c.  when  polished. 


8 


OPERATIVE  MASONRY. 


Both  granular  and  compact  lime  stone  furnish  numerous  varieties 
of  marble;  but  those,  which  belong  to  the  former  exhibit,  a  more 
uniform  color,  are  generally  susceptible  of  a  higher  polish,  and  are 
hence  most  esteemed  for  statuary  and  some  other  purposes.  The 
uniformity  of  color,  so  common  in  primitive  marbles,  is  sometimes 
interrupted  by  spots,  or  veins,  or  clouds,  of  different  colors,  arising 
from  the  intermixture  of  hornblende,  serpentine,  &c.  Among  the 
foreign  marbles  we  may  mention, 

The  Carrara  Marble.  Found  at  Carrara,  in  Tuscany.  It  was 
highly  esteemed  by  the  ancients  ;  and  is  at  present  more  employed 
by  the  Italian  artist,  than  any  other  kind  for  statuary,  vases,  slabs 
for  household  furniture,  &c.  It  is  very  white,  sometimes  veined 
with  gray,  and  has  a  grain  considerably  line.  In  the  centre  of  the 
blocks  of  this  marble  very  limpid  rock  crystals  are  found,  which 
are  called  Carrara  diamonds.  The  average  price  of  this  marble  is 
ten  or  twelve  dollars  a  cubic  foot. 

The  Luni  Marble.  Found  also  in  Tuscany,  is  extremely  white, 
and  its  grain  is  a  little  finer,  than  that  of  Carrara.  Of  this  marble 
it  is  generally  supposed,  the  famous  Apollo  Belvidere,  in  the  Vati- 
can at  Rome,  is  made,  as  well  as  the  Antinous  of  the  capitol,  and 
the  Antinous  in  bas-relief  in  the  Napoleon  museum. 

The  Parian  Marble.  Obtained  from  the  islands  of  Paros,  Naxos, 
&c.  in  the  Archipelago,  was  much  employed  by  the  ancients.  It  is 
white,  but  often  with  a  slight  tinge  of  yellow.  Its  grains  are  larger 
than  those  of  the  Carrara  marble.  The  celebrated  Venus  de  Medi- 
cis,  in  the  gallery  at  florence,  is  of  this  marble.  It  was  called  by 
the  ancients  Lychnites,  in  consequence  of  its  quarries  being  often 
worked  by  the  light  of  a  lamp.  It  is  on  Parian  marble  that  the 
celebrated  tables  at  Oxford  are  inscribed. 

The  Pentelic  Marble.  From  mount  Penteles,  near  Athens.  This 
marble  much  resembles  the  preceding,  but  is  more  dense  and  fine- 
grained ;  it  sometimes  exhibits  faint  greenish  zones,  produced  by 
greenish  talc,  whence  the  Italian  name  Cipilino  statuario.  The 
principal  monuments  of  Athens  were  of  Pentelic  marble,  such  as 
the  Parthenon,  the  Propylees,  and  the  Hippodrome.  Among  the 
statues  of  this  marble  in  the  Napoleon  museum,  at  Paris,  are  the 
Torso  ;  a  Bacchus  in  repose  ;  a  Jason,  (called  Cincinnatus,)  a  Paris  ; 
the  Discobolus  reposing ;  the  bas-relief,  known  by  the  name  of  the 
Sacrifice ;  the  throne  of  Saturn  ;  the  Tripod  of  Apollo  ;  and  the 
two  beautiful  Athenian  inscriptions  known  by  the  name  of  "  Nointel 
Marbles,"  because  M.  Nointel  caused  them  to  be  brought  from 
Athens  to  Paris  in  1672. 

Greek  White  marble.  The  marble  to  which  the  statuaries  of 
Rome  give  the  name  of  Marmo  Greco,  is  of  a  very  bright  snow 
white  color,  close  and  fine-grained,  and  of  a  hardness,  which  is 
rather  superior  to  that  of  other  white  marbles.  It  takes  a  very  fine 
polish.  It  has  been  called  corallic  marble,  from  being  found  near 
the  river  Coralus,  in  Phrigia.  According  to  Pliny,  it  was  found  in 
Asia,  in  masses  of  small  dimensions ;  and  it  is  said,  that  a  similar 


OF  MARBLE. 


9 


kind  occurs  on  mount  Canuto,  near  Palermo,  in  Sicily.  The  Greek 
marble  was  obtained  from  several  islands  in  the  Archipelago  ;  such 
as  Scio,  Samos,  &c.  Among  the  statues  of  this  marble  in  the  Na- 
poleon museum,  are  a  Bacchus,  and  Zeno  the  philosopher. 

Translucid  White  Marble.  This  much  resembles  Parian  marble, 
but  differs  from  it  as  being  more  translucid.  There  are,  at  Venice, 
and  several  other  towns  in  Lombardy,  columns  and  altars  of  this 
marble,  the  quarries  of  which  are  perfectly  unknown. 

Flexible  White  Marble.  It  is  of  a  beautiful  white  color,  and  fine 
grain.  There  are  five  or  six  tables  of  it  preserved  in  the  house  of 
the  prince  Borghese,  at  Rome.  They  were  dug  up,  as  the  Abbe 
Fortis  was  told,  in  the  field  of  Mondragone.  Being  set  on  end  they 
bend,  accillating  backward  and  forward,  when  laid  horizontally, 
they  form  a  curve. 

White  Marble  of  mount  Hymettus.  This  is  not  a  very  pure  white 
variety,  but  inclines  a  little  to  gray.  Pliny  informs  us  that  Lucius 
Crassus,  the  orator,  was  exposed  to  the  sarcasms  of  Marcus  Brutus, 
because  he  had  adorned  his  house  with  six  columns,  twelve  feet 
high,  of  the  Hymettian  marble.  The  statue  of  Meleager,  in  the 
Napoleon  museum,  is  of  this  marble. 

These  are  the  chief  white  marbles,  which  the  ancients  used  for 
the  purposes  of  Architecture  and  Sculpture. 

Black  Antique  Marble.  (Nero  Antico,  of  the  Italians.)  This  dif- 
fers from  the  modern  black  marbles,  by  the  superior  intensity  of  its 
color.  It  has  been  said  that  the  ancients  procured  this  marble  from 
Greece,  but  it  has  been  ascertained  that  quarries  of  real  antique 
black  marble  have  been  re-discovered,  which  were  wrought  by  the 
ancients,  and  of  which  the  remains  are  still  to  be  seen,  at  the  distance 
of  two  leagues  from  Spa,  towards  Franchimont,  not  far  from  Aix-la 
Chapelle.  This  marble  is  extremely  scarce,  and  occurs  only  in 
wrought  pieces. 

Red  Antique  Marble.  (Rosso  Antico,  of  the  Italians.)  This  beau- 
tiful marble  is  of  a  deep  blood-red  color,  here  and  there  with  white 
veins,  and  if  closely  examined,  is  found  to  be  sprinkled  over  with 
minute  white  dots,  as  if  it  were  strewed  sand.  Of  this  kind  is  the 
Egyptian  Antinous,  in  the  museum  at  Paris.  But  the  most  esteemed 
variety  of  Rosso  Antico  is  that  of  a  very  deep  red,  without  any 
veins,  such  as  it  is  seen  in  the  two  antique  chairs,  and  in  the  bust  of 
an  Indian  Bacchus  in  the  same  museum.  The  white  spots,  or  points, 
which  are  never  wanting  in  the  true  red  antique,  distinguish  it  from 
others  of  the  same  color.  It  is  not  known  from  whence  the  ancients 
obtained  this  marble  ;  the  conjecture  is  that  it  was  brought  from 
Egypt.  There  is,  in  the  Grimani  Palace,  at  Venice,  a  colossal 
statue  of  Marcus  Agrippa,  in  Rosso  Antico,  which  was  formerly 
preserved  in  the  Pantheon,  at  Rome. 

Green  Antique  Marble.  (The  verde  Antico  of  the  Italians.)  This 
may  be  considered  a  kind  of  Breccia,  the  paste  of  which  is  a  mix- 
ture of  talc  and  limestone  ;  and  the  dark  green  fragments  are  owing 
to  serpentine  more  or  less  pure.    The  verde  antico  of  the  best  qual- 


10 


OPERATIVE  MASONRY. 


ity  is  that  of  which  the  paste  is  of  a  grass  green,  and  the  blackish 
spots  are  of  that  variety  of  serpentine,  which  is  called  noble  serpen- 
tine. This  marble  is  much  esteemed  in  commerce,  but  large  pieces 
of  a  fine  quality  are  seldom  seen.  There  are  four  fine  columns  of 
it  in  the  Napoleon  museum ;  but  much  more  beautiful  ones  are 
preserved  at  Parma.  This  verde  antico  must  not  be  confounded 
with  the  marbles  known  by  the  names  of  vert-de-mer  or  vert-d'- Egypt. 
The  real  verde  antico  is  a  breccia,  and  is  never  mingled  with  red 
spots,  while  those  just  mentioned  are  veined  marbles  mixed  with  a 
dull  red  substance,  which  gives  them  a  brownish  hue. 

Red  spotted  green  Antique  Marble.  Its  ground  is  very  dark  green, 
here  and  there  marked  with  small  red  and  black  spots.  The  quar- 
ries of  this  marble  are  lost,  and  it  is  found  only  in  small  pieces, 
which  are  made  into  tablets,  &c. 

Leek  Marble.  (Marbre  poireau  of  the  French  lapidaries.)  This 
is  a  mixture  of  limestone  and  a  talcose  substance  of  light  green,  sha- 
ded with  blackish  green,  and  related  to  serpentine.  Its  texture  is 
filamentose,  and  as  it  were  ligneous ;  its  fragments  are  splintery. 
When  polished  it  exhibits  long  green  veins.  Like  all  other  talcose 
marbles,  it  soon  decomposes  in  the  open  air.  There  is  a  table  of  it 
in  the  hotel  de  la  Monnoie,  at  Paris.    Its  quarries  are  lost. 

Marble  petit  Antique.  Of  the  French  Lapidaries.  It  is  traversed 
with  white  and  grey  veins,  the  two  colors  being  disposed  in  uninter- 
rupted threads  ;  the  tables  made  of  this  marble  are  irregularly 
striped  their  whole  length,  which  has  a  very  fine  effect.  It  is 
much  esteemed,  and  only  made  use  of  for  inlaying  ornamental  fur- 
niture.   Its  quarries  are  unknown. 

Yellow  Antique  Marble.  (Giallo  Antico\  of  the  Italians.)  Of  this 
there  are  three  varieties.  The  first  has  more  or  less  the  color  of 
the  yolk  of  an  egg,  and  is  nearly  of  an  uniform  tint ;  the  other  is 
marked  with  black  or  deep  yellow  rings,  and  the  last  is  merely  a 
paler  colored  variety  of  the  first.  These  different  marbles,  for  which 
the  Sienna  marble  is  a  good  substitute,  are  found  only  in  small  de- 
tached pieces,  and  in  antique  inlaid  work.  It  is  in  this  manner 
that  the  two  tables  of  Lazulite  in  the  Napoleon  museum  are  sur- 
rounded with  a  border  of  the  deep  yellow  variety. 

Grand  Antique  Marble.  This  variety,  which  is  a  breccia,  con- 
taining some  shells,  consist  of  large  fragments  of  a  black  marble 
united  by  veins  or  lines  of  shining  white.  This  superb  marble, 
the  quarries  of  which  are  lost,  is  sometimes  found  in  detached 
pieces  and  wrought.  There  are  four  columns  of  it  in  the  museum 
at  Paris.  A  less  valuable  variety  is  that  in  which  the  spots,  instead 
of  being  an  entire  intense  black,  are  of  a  gray  color. 

Antique  Cipolin  Marble.  Cipolin  is  a  name  given  to  all  such 
marbles  as  have  greenish  zones,  caused  by  green  talc  ;  their  fracture 
is  granular  and  shining,  and  shows  here  and  there  plates  of  tale. 
They  are  never  found  to  contain  marine  bodies.  The  ancients  have 
made  frequent  use  of  Cipolin.  It  takes  a  fine  polish,  but  its  ribbon- 
like stripes  always  remain  dull,  and  are  that  part  of  the  marble, 


OF  MARTU/E. 


11 


which  first  decomposes,  when  exposed  to  the  open  air.  There  are 
modern  Cipolins  as  fine  as  that  used  by  the  ancients. 

Purple  Antique  Breccia  Marble.  This  should  not  be  confounded 
with  African  Breccia.  There  is,  perhaps,  no  marble,  the  color  and 
spots  of  which  are  so  variable  as  that  of  the  violet  Breccia.  The 
following  are  the  chief  varieties.  The  first  is  that  from  which  the 
name  of  the  marble  is  derived  ;  it  has  a  purplish  brown  base,  in 
which  are  imbedded  large  angular  fragments  of  a  light  purple 
color,  and  others  of  a  white  color.  This  first  variety  can  be  em- 
ployed only  in  large  works,  on  account  of  the  size  of  its  spots, 
which  are  sometimes  a  foot  in  diameter.  There  is  a  beautiful  table 
of  it  in  the  Napoleon  museum.  The  second  variety  is,  as  it  were, 
the  miniature  of  the  first ;  it  exhibits  the  same  spots,  but  within  a 
much  narrower  compass,  so  that  it  may  be  used  for  less  gigantic 
works,  than  those  for  which  the  other  is  employed.  The  third 
variety  is  known  in  commerce  by  the  name  of  rose  colored  marble  ; 
in  this,  the  spots,  instead  of  being  white  and  light  purple,  have  a 
pleasing  rose  color.  It  is  scarce,  and  never  seen  in  large  pieces. 
The  fourth,  which  is  the  most  beautiful,  appears,  at  first  view,  to 
be  perfectly  distinct  from  the  others,  but  it  is,  nevertheless,  a  mere 
variety  of  the  purple  breccia.  Its  ground  is  of  a  yellowish  green 
color,  and  the  spots,  which  are  of  various  sizes,  are  white,  green, 
purplish  and  yellow,  mottled  with  red  ;  these  various  spots  are 
traversed  by  straight  lines  of  grayish  white  color.  This  fourth  va- 
riety is  very  scarce.  There  are,  however,  two  tables  of  it  at  Paris, 
in  the  possession  of  private  individuals. 

African  Breccia  Marble.  Its  ground  is  black,  variegated  with 
large  fragments  of  a  grayish  white,  of  a  deep  red,  or  of  purplish 
wine  color  ;  but  these  latter  are  always  smaller  than  the  former. 
This  is  one  of  the  most  beautiful  marbles  existing,  and  has  a  superb 
effect  when  accompanied  by  gilt  ornaments.  Though  rather  less 
vivid  in  its  colors  than  the  preceding  violet  breccia,  it  is  yet,  on 
the  whole,  more  beautiful.  Whether  Africa  is  the  part  of  the 
world  where  it  is  found,  as  its  name  implies,  is  not  certain.  The 
pedestal  of  Venus  leaving  the  bath,  and  a  large  column,  both  in  the 
Napoleon  museum,  are  of  this  marble. 

There  are  other  varieties  of  breccia  marble,  not  differing  materi- 
ally from  those  already  described  ;  they  are,  many  of  them,  very 
beautiful,  but  very  scarce,  found  only  in  small  pieces,  among  the 
ruins  at  Rome. 

Marbles  are  found  abundantly,  and  in  variety,  in  all  countries. 
There  are  many  curious  varieties  in  the  United  States.  The  chief 
quarries  that  have  been  noticed  are  the  following  : 

Stockbridge  &  Lanesborough  Marble.  In  Berkshire  County,  Massa- 
chusetts.   Its  grain  is  somewhat  coarse,  and  its  color  white,  some- 

[The  term  breccia,  which  has  often  been  used  in  the  preceding  pages,  is 
applied  to  an  aggregate,  composed  of  angular  fragments  of  the  same,  or  differ- 
ent .minerals,  united  by  some  cement,  sometimes,  however,  a  few  of  the  frag- 
ments are  a  little  rounded.  The  different  fragments  always  present  a  variety 
of  colors.  There  are  several  varieties,  some  of  which  are  susceptible  of  a  fine 
polish.] 

vtoqa  r9fd"iiim  Aoxld  onft        'to  vTuwp  B  ai  ^ihoY-waW  to  'date  fjdi 


13 


OPERATIVE  MASONRY. 


times  with  a  slight  tinge  of  blue.  A  quarry  has  also  been  opened 
of  a  similar  kind  of  marble,  at  Pittsfield,  in  the  same  county. 

Vermont  Marble.  It  is  found  of  various  qualities,  according  to 
Professor  Hall,  in  many  places  on  the  west  side  of  the  green  moun- 
tains. A  few  years  since,  a  valuable  quarry  was  found  in  Middle- 
burgh,  on  Otter  Creek,  eleven  miles  above  Vergennes.  The 
quarry  forms  one  bank  of  the  creek  for  several  roods,  and  extends 
back  into  the  side  of  a  hill,  to  a  distance  at  present  unknown.  The 
stone  lies  in  irregular  strata,  varying  considerably  in  thickness,  but 
all  more  or  less  inclined  to  the  north-west.  The  marble  is  of 
different  colors  in  different  parts  of  the  bed.  On  one  side,  it  is  of 
a  pure  white,  and  of  a  quality,  if  at  all,  but  little  inferior  to  the 
Italian  marble  ;  but  this  seems  to  constitute  but  a  small  portion  of 
the  whole  mass.  The  color  that  predominates  through  most  parts 
of  the  quarry  is  a  gray  of  different  intensities.  The  marble  of  both 
kinds  is  solid,  compact,  free  from  veins  of  quartz,  and  susceptible 
of  an  excellent  polish.  A  mill  of  peculiar  construction  has  been 
erected  for  the  purpose  of  sawing  the  stone  into  slabs.  It  contains 
sixty  five  saws,  which  are  kept  almost  in  continual  operation. 
Daring  the  years  of  1809  and  1810  these  saws  cut  out  20,000  feet 
of  slabs,  and  the  sales  of  marble  tables,  side-boards,  tomb-stones, 
&c.  in  the  same  period,  amounted  to  about  11,000  dollars. 

Some  of  the  Vermont  marbles  are  as  white  as  the  Carrara  marble, 
with  a  grain  intermediate  between  that  of  the  Carrara  and  Parian 
marbles. 

New  Haven  Marble.  The  texture  of  this  very  beautiful  marble 
is  granular,  but  very  fine.  Its  predominant  colors  are  gray  and 
bl  le,  richly  variegated  by  veins  or  clouds  of  white,  black,  or  green  ; 
i  a  dead,  the  green  often  pervades  a  large  mass.  It  takes  a  high  pol- 
i  \,  a  t'd  e  uLires  the  action  of  fire  remarkably  well.  This  marble 
c  o  it  -tins  cnroinite  of  irou,  magnetic  oxide  of  iron,  and  serpentine  ; 
hence  it  resembles  the  vert  antique,  and  is,  perhaps,  the  only  marble 
of  the  kind  hitherto  discovered  in  America. 

Tkomastown  Marble.  From  Lincoln  County,  Maine.  It  is,  in  gen- 
eral, fine-grained}  and  its  colors  are  often  richly  variegated.  Some- 
ti  lie  it  is  white,  or  grayish-white,  diversified  with  veins  of  a  dif- 
ferent color.  But,  in  the  finest  pieces,  the  predominant  color  is 
gray,  or  bluish-gray,  interrupted  with  whitish  clouds,  which,  at  a 
small  distance,  resemble  the  minutely  shaded  parts  of  an  engraving, 
and,  at  the  same  time,  traversed  by  innumerable  small  and  irregular 
veins  of  black  and  white.  It  recieves  a  fine  polish,  and  is  well 
fitted  for  ornamental  works. 

Some  of  the  white  marble  of  Vermont,  and  that  which  may  be 
obtained  at  Smithfield,  in  Rhode-Island,  more  peculiarly  deserve 
the  name  of  statuary  marble. 

Flexible  Marble,  has  been  observed  at  Pittsford,  Rutland  county, 
Vermont ;  and  at  Pittsfield  in  Massachusetts. 

Pennsylvania  Marble.  There  is  found  at  Aaronsburg,  in  Northum- 
berland county,  a  black  marble.  It  is  of  compact  limestone,  con- 
taining white  specks.  At  Marbletown,  near  the  Hudson  river,  in 
the  state  of  New-York,  is  a  quarry  of  very  fine  black  marble,  spot- 


OF  MARBLE. 


13 


ted  with  white  shells.  Marble  has  also  been  found  in  Virginia,  and 
some  other  of  the  United  States.  But  the  state  of  the  arts  has  not, 
hitherto,  directed  the  attention  of  the  curious  so  much  to  this  sub- 
ject as  it  intrinsically  deserves. 


SECTION  II.  The  Polishing  of  Marble. 

The  art  of  cutting  and  polishing  marble  was,  of  course,  known 
to  the  ancients,  whose  mode  of  proceeding  appears  to  have  been 
nearly  the  same  with  that  employed  at  present ;  except,  perhaps, 
that  they  were  unacquainted  with  those  superior  mechanical  means, 
which  now  greatly  facilitate  the  labor,  and  diminish  the  expense  of 
the  articles  thus  produced.  There  are  many  manufactories  of  1 1 1 1 ^ 
kind,  generally  called  marble  mills,  on  the  continent,  and  al  o  in 
Great  Britain  ;  but  as  the  principle  on  which  they  proceed  is  r  eaily 
the  same  in  all,  it  will  suffice  in  this  place  to  give  the  desciiption  of 
one  or  two  of  the  latter. 

An  essential  part  of  the  art  of  polishing  marble  is  the  i  hoice  of 
substances  by  which  the  prominent  parts  are  to  be  removed.  Ihe 
first  substance  should  be  the  sharpest  sand,  so  as  to  cut  as  fast  as 
possible,  and  this  is  to  be  used  till  the  surface  becomes  perfectly  fat. 
After  this,  the  surface  is  rubbed  with  a  finer  sand,  and  frequently 
with  a  third.  The  next  substance,  after  the  finest  sand,  is  emery  of 
different  degrees  of  fineness.  This  is  followed  by  the  red  powder 
called  tripoli,  which  owes  its  cutting  quality  to  the  oxide  of  iron  it 
contains.  Common  iron-stone,  powdered  and  levigated,  answers  the 
purpose  very  well.  This  last  substance  gives  a  tolerably  line  polish. 
This,  however,  is  not  deemed  sufficient.  The  last  polish  is  given 
with  putty.  After  the  first  process,  which  merely  takes  away  the 
inequalities  of  the  surface,  the  sand  employed  in  preparing  it  for  the 
emery  should  be  chosen  of  an  uniform  quality.  If  it  abounds  with 
some  particles  harder  than  the  rest,  the  surface  will  be  liable  to  be 
scratched  so  -deep  as  not  to  be  removed  by  the  emery.  In  order  to 
get  the  sand  of  uniform  quality,  it  should  be  levigated  and  washed. 
The  hard  particles  being  generally  of  a  different  specific  gravity  to 
the  rest,  may,  by  this  means,  be  separated.  This  method  will  be 
found  much  superior  to  that  of  sifting.  The  substance  by  which 
the  sand  is  rubbed  upon  the  marble  is  generally  an  iron  plate,  es- 
pecially for  the  first  process.  A  plate  of  an  alloy  of  lead  and  tin  is 
better  for  the  succeeding  processes,  with  the  fine  sand  and  emery. 
The  rubbers  used  for  the  polishing,  or  last  process,  consist  of  coarse 
linen  cloths,  such  as  hop  bagging,  wedged  tight  into  an  iron  plane. 
In  all  of  these  processes,  a  constant  supply  of  water,  in  small  quanti- 
ties, is  absolutely  necessary. 

The  sawing  of  marble  is  performed  on  the  same  principles  as  the 
first  process  of  polishing.  The  saw  is  of  soft  iron,  and  is  contin- 
ually supplied  with  water  and  the  sharpest  sand. 

Marble  is  extensively  used  for  building,  statuary,  decorations  and 
inscriptions.    In  warm  countries  it  is  one  of  the  most  durable  of 


14 


OPERATIVE  MASONRY. 


substances,  as  is  proved  by  tbe  edifices  of  Athens,  which  have  re- 
tained their  polish  for  more  than  two  thousand  years.  Severe  frost, 
preceded  by  moisture,  causes  it  to  crack  and  scale,  great  heat  re- 
duces it  to  quick-lime.  It  may  be  burnt,  like  other  varieties  of 
lime-stone,  into  lime  for  preparing  mortar,  or  employed  as  a  flux 
for  certain  ores,  particularly  those  which  contain  alumine  and  silex. 

White  marble  is  sometimes  cleaned  by  muriatic  acid  diluted  with 
water.  Spots  of  oil  stain  white  marble,  so  that  they  cannot  be 
taken  out. 


SECTION  III.  Artificial  Marble. 

The  stucco,  whereof  they  make  statues,  busts,  basso  relievos,  and 
other  ornaments  of  architecture,  ought  to  be  marble  pulverized, 
mixed  in  a  certain  proportion  with  plaster  ;  The  whole  well  sifted, 
worked  up  with  water,  and  used  like  common  plaster.  [Set 
Stucco.] 

There  is  also  a  kind  of  artificial  marble,  made  of  flake  selenites, 
or  a  transparent  stone  resembling  the  plaster  ;  which  becomes  very 
hard  and  receives  a  tolerable  polish,  and  may  deceive  the  eye. 
This  kind  of  selenites  resembles  Muscovy  talc.  There  is  another 
sort  of  artificial  marble,  formed  by  corrosive  tincture,  which,  pen- 
etrating into  white  marble,  to  the  depth  of  a  line  or  more,  imitates 
the  various  colors  of  other  dearer  marbles.  There  is  also  a  prepa- 
ration of  brimstone  in  imitation  of  marble.  To  do  this,  you  must 
provide  yourself  with  a  flat  and  smooth  piece  of  marble.  On  this 
make  a  border  or  wall,  to  encompass  either  a  square  or  oval  table, 
which  may  be  done  either  with  wax  or  clay.  Then,  having  provided 
several  sorts  of  colors,  as  white-lead,  vermillion,  lake,  orpiment, 
masticot,  Prussian-blue,  &c.  melt,  on  a  slow  fire,  some  brimstone, 
in  several  glazed  pitkins  ;  put  one  particular  sort  of  color  into  each, 
and  stir  it  well  together  ;  then  having  before  oiled  the  marble  all 
over  within  the  wall,  with  one  color  quickly  drop  spots  upon  it 
of  larger  and  less  size  ;  after  this  take  another  color,  and  do  as  be- 
fore ;  and  so  on,  till  the  stone  is  covered  with  spots  of  all  the  colors 
you  design  to  use.  When  this  is  done,  you  are  next  to  consider 
what  color  the  mass,  or  ground  of  your  table  is  to  be  ;  if  of  a  grey 
color,  then  take  fine  sifted  ashes,  and  mix  them  up  with  melted 
brimstone,  or  if  red,  with  English  red  ochre  ;  if  white,  with  white 
lead  ;  if  black,  with  lamp  or  ivory  black.  Your  brimstone  for  the 
ground  must  be  pretty  hot,  that  the  colored  drops  on  the  stone  may 
unite  and  incorporate  with  it.  When  the  ground  is  poured  even  all 
over,  you  are  next,  if  judged  necessary,  to  put  a  thin  wainscot  board 
upon  it ;  this  must  be  done  while  the  brimstone  is  hot,  making  also 
the  board  hot,  which  ou^ht  to  be  thoroughly  dry,  in  order  to  cause 
the  brimstone  to  stick  the  better  to  it.  When  the  whole  is  cold, 
take  it  up,  and  polish  it  with  a  cloth  and  oil,  and  it  will  look  very 
beautiful. 


OF  MARBLE. 


15 


SECTION  IV.-  The  Coloring  of  Marble. 

The  coloring  of  marble  is  a  nice  art,  and  in  order  to  succeed  in 
it,  the  pieces  of  marble,  on  which  the  experiments  are  tried,  must 
be  well  polished,  and  clear  from  the  least  spot  or  vein.  The  harder 
the  marble  is,  the  better  it  will  be,  and  the  greater  the  heat  necessa- 
ry in  the  operation  ;  therefore,  alabaster,  and  the  common  soft  white 
marble  are  very  improper  to  perform  these  operations  upon. 

Heat  is  always  necessary,  for  the  opening  of  the  pores,  so  as  to 
render  it  fit  to  receive  the  colors ;  but  the  marble  must  never  be 
made  red  hot,  for  then  the  texture  of  the  marble  itself  is  injured 
and  the  colors  are  burnt,  and  lose  their  beauty.  Too  small  a  de- 
gree of  heat  is  as  bad  as  too  great  ;  for,  in  this  case,  though  the 
marble  receives  the  color,  it  will  not  be  fixed  in  it,  nor  strike  deep 
enough.  Some  colors  will  strike  even  cold  ;  but  they  are  never  so 
well  sunk  in  as  when  a  just  degree  of  heat  is  used.  The  proper  de- 
gree is  that,  which,  without  making  the  marble  red,  will  make  the 
liquor  boil  on  its  surface.  The  menstruums  used  to  strike  in  the 
colors,  must  be  varied  according  to  the  nature  of  the  color  to  be 
used.  A  lixivium  made  of  horses  or  dog's  urine,  with  four  parts  of 
quick  lime,  and  one  part  pot-ashes,  is  excellent  for  some  colors  ; 
common  ley,  of  wood  ashes,  does  very  well  for  others  ;  for  some, 
spirit  of  wine  is  best,  and  finally,  for  others,  oily  liquors,  or  com- 
mon white  wine. 

The  colors  which  have  been  found  to  succeed  best  with  the  pecu- 
liar menstruums,  are  these  :  stone-blue  dissolved  in  six  times  the 
quantity  of  spirit  of  wine,  or  of  the  urinous  lixivium,  and  that  color, 
which  the  painters  call  litmus,  dissolved  in  common  ley,  of  wood 
ashes.  An  extract  of  saffron,  and  that  color  made  of  buckthorn 
berries,  and  called  by  the  painters  soap-green,  both  succeed,  well 
dissolved  in  urine  and  quick-lime,  and  tolerably  well  in  spirit  of 
wine.  Vermilion,  and  a  fine  powder  of  cochineal,  succeed  also 
very  well  in  the  same  liquors.  Dragon's  blood  succeeds  very  well 
in  spirit  of  wine,  as  does  also  a  tincture  of  logwood  in  the  same 
spirit.  Alkanet  root  gives  a  fine  color,  but  the  only  menstruum  to 
be  used  for  this  is  oil  of  turpentine  ;  for  neither  spirit  of  wine,  nor 
any  lixivium  will  do  with  it.  There  is  a  kind  of  substance,  called 
dragon's  blood  in  tears,  which,  mixed  with  urine  alone,  gives  a  very 
elegant  color. 

Besides  these  mixtures  of  colors,  and  menstruums,  there  are  some 
colors,  which  are  to  be  laid  on  dry  and  unmixed.  These  are  drag- 
on's blood  of  the  purest  kind,  for  a  red  ;  gamboge,  for  a  yellow  ; 
green  wax,  for  a  green  ;  common  brimstone,  pitch  and  turpentine, 
for  a  brown  color.  The  marble,  for  these  experiments,  must  be 
made  considerably  hot,  and  the  colors  are  to  be  rubbed  on  dry,  in 
the  lump.  Some  of  these  colors,  when  once  given,  remain  immu- 
table ;  others  are  easily  changed  or  destroyed.  Thus  the  red  color, 
given  by  dragon's  blood,  or  by  the  decoction  of  logwood,  will  be 


16 


OPERATIVE  MASONRY. 


wholly  taken  away  by  oil  of  tartar,  and  the  polish  of  the  marble 
not  hurt  by  it. 

A  fine  gold  color  is  given  in  the  following  manner  :  take  crude 
sal-ammoniac,  vitriol,  and  verdigris,  of  each,  equal  quantities  ; 
white  vitriol  succeeds  best,  and  all  must  be  thoroughly  mixed  in 
fine  powder. 

The  staining  of  marble,  to  all  degrees  of  red,  or  yellow,  by  solu- 
tion of  dragon's  blood  or  gamboge,  may  be  done  by  reducing  these 
gums  to  powder,  and  grinding  them  with  the  spirit  of  wine,  in  a 
glass  mortar  ;  but  for  smaller  attempts,  no  method  is  so  good  as  the 
mixing  a  little  of  either  of  these  powders  with  spirit  of  wine,  in  a 
silver  spoon,  and  holding  it  over  burning  charcoal.  By  this  means, 
a  fine  tincture  will  be  extracted,  and  with  a  pencil  dipped  in  this, 
the  finest  traces  may  be  made  on  the  marble,  while  cold,  which,  on 
heating  of  it  afterwards,  either  on  sand,  or  in  a  baker's  oven,  will 
all  sink  very  deep,  and  remain  perfectly  distinct  in  the  stone.  It  is 
very  easy  to  make  the  ground  color  of  the  marble  red  or  yellow,  by 
this  means,  and  leave  white  veins  in  it.  This  is  to  be-done  by  cov- 
ering the  places  where  the  whiteness  is  to  remain  with  some  white 
paint,  or  even  with  two  or  three  doubles  only  of  paper,  either  of 
which  will  prevent  the  color  from  penetrating  in  that  part.  All 
the  degrees  of  red  are  to  be  given  to  the  marble  by  the  means  of 
this  gum  alone  ;  a  slight  tincture  of  it,  without  the  assistance  of 
heat  to  the  marble,  gives  only  a  pale  flesh  color  ;  but  the  stronger 
tinctures  give  it  yet  deeper.  To  this  the  assistance  of  heat  adds  yet 
greatly  ;  and  finally,  the  addition  of  a  little  pitch,  to  the  tincture, 
gives  it  a  tendency  to  blackness,  or  any  degree  of  deep  red  that 
is  desired. 

A  blue  color  may  be  given  to  marble,  by  dissolving  turnsol  in  a 
lixivium  of  lime  and  urine,  or  in  the  volatile  spirit  of  urine  ;  but 
this  has  always  a  tendency  to  purple,  whether  made  by  one  or  the 
other  of  these  ways.  A  better  blue,  and  used  in  an  easier  manner, 
is  furnished  by  the  Canary  turnsol,  a  substance  well  known  among 
the  dyers.  This  need  only  be  dissolved  in  water,  and  drawn  on 
the  place  with  a  pencil ;  this  penetrates  very  deep  into  the  marble, 
and  the  color  may  be  increased  by  drawing  the  pencil,  wetted 
afresh,  several  times  over  the  same  lines.  This  color  is  subject  to 
spread  and  diffuse  itself  irregularly  ;  but  it  may  be  kept  in  regular 
bounds,  by  circumscribing  its  lines  with  beds  of  wax,  or  any  other 
substance.  It  is  to  be  observed,  that  this  color  should  always  be 
laid  on  cold,  and  no  heat  given  ever  afterwards  to  the  marble  ;  and 
one  great  advantage  of  this  color  is,  that  it  is  easily  added  to  mar- 
bles already  stained  with  any  other  colors,  and  it  is  a  very  beautiful 
ting;e,  and  lasts  a  long  time. 

This  art  has,  in  several  persons'  hands,  been  a  very  lucrative  secret, 
though  there  is  scarcely  any  thing  in  it,  that  has  not,  at  one  time  or 
another,  been  published. 

Kircher  has  the  honor  of  being  one  of  the  first  who  published 
anything  practicable  about  it.  This  author  meeting  with  stones  in 
some  cabinets,  supposed  to  be  natural,  but  having  figures  too  nice 
and  particular  to  be  supposed  to  be  nature's  making,  and  these  not 
only  on  the  surface,  but  sunk  through  the  whole  body  of  the  stones, 


OF  GRANITE.  17 

was  at  the  pains  of  finding  out  the  artist,  who  did  the  business  ;  and 
on  his  refusing  to  part  with  the  secret  on  any  terms,  this  author, 
with  Albert  Gunter,  a  Saxon,  endeavored  to  find  it  out.  Their 
method  is  this.  Take  aqua  fortis  and  aqua  regia,  of  each  one  ounce, 
sal-ammoniac  one  ounce,  spirit  of  wine  two  drachms,  about  twenty- 
six  grains  of  gold,  and  two  drachms  of  pure  silver  ;  let  the  silver 
be  calcined  and  put  into  a  phial,  and  pour  upon  it  the  aqua  fortis  ; 
let  this  stand  some  time,  then  evaporate  it,  and  the  remainder  will 
at  first  appear  of  a  blue,  and  afterwards  of  a  black  color  ;  then  put 
the  gold  into  another  phial,  and  pour  the  aqua  regia  upon  it,  and 
when  it  is  dissolved,  evaporate  it  as  the  former  ;  then  put  the  spirit 
of  wine  upon  the  sal-ammoniac,  and  let  it  be  evaporated  in  the  same 
manner.  All  the  remainders,  and  many  others  made  in  the  same 
manner  from  other  metals,  dissolved  in  their  proper  acid  menstrua, 
are  to  be  kept  separate,  and  used  with  a  pencil  on  the  marble  : 
These  will  penetrate  without  the  least  assistance  of  heat,  and  the 
figure  being  traced  with  a  pencil  on  the  marble,  the  several  parts 
are  to  be  -touched  over  with  the  proper  colors,  and  this  renewed 
daily,  till  the  colors  have  penetrated  to  the  desired  depth  into  the 
stone. 

After  this,  the  mass  may  be  cut  into  thin  plates,  and  every  one 
of  them  will  have  the  figure  exactly  represented  on  both  surfaces, 
the  colors  never  spreading. 

The  nicest  method  of-  applying  these,  or  the  other  tinging  sub- 
stances, to  marble  that  is  to  be  wrought  into  any  ornamental  works, 
and  where  the  back  is  not  exposed  to  view,  is  to  apply  the  colors 
behind,  and  renew  them  often,  till  the  figure  is  sufficiently  seen 
through  the  surface  on  the  front,  though  it  does  not  quite  extend 
to  it.  This  is  the  method,  that,  of  all  others,  brings  the  stone  to  a 
nearer  resemblance  of  natural  veins  of  this  kind.  The  same  author 
gives  another  method  to  color  marble,  by  vitriol,  bitumen,  &c. 
forming  a  design  of  what  you  like  upon  paper,  and  laying  the  said 
design  between  two  pieces  of  polished  marble  ;  then  closing  all  the 
interstices  with  wax,  you  bury  them  for  a  month  or  two  in  a  damp 
place.  On  taking  them  up,  you  will  find  that  the  design  you  paint- 
ed on  the  paper  has  penetrated  the  marbles,  and  formed  exactly 
the  same  design  upon  them. 


SECTION  V.  Granite. 

Granite  is  apparently  the  oldest  and  deepest  of  rocks.  It  is  one 
of  the  hardest  and  most  durable  which  have  been  wrought,  and  is 
obtained  in  larger  pieces  than  any  other  rock.  Granite  is  a  com- 
pound stone,  varying  in  color  and  coarseness.  It  consists  of  three 
constituent  parts,  united  to  each  other  without  the  intervention  of 
any  cement,  viz.  quartz,  the  material  of  rock  crystal  ;  feldspar,  which 
gives  it  its  color  ;  and  lastly  mica,  a  transparent,  thin,  or  foliated 
substance. 

But  in  order  to  understand  more  perfectly  the  nature  and  qualities 
of  granite,  some  examination  of  its  constituent  parts  is  necessary. 


18 


OPERATIVE  MASONRY. 


1.  Quartz  belongs  to  that  class  of  minerals,  denominated  earthy  cowt- 
pounds,  or  stones.  It  embraces  numerous  varieties,  differing  much 
in  their  forms,  texture,  and  other  external  characters.  And 
although  but  few  well  defined  external  characters  apply  to  the 
whole  species,  yet  most  of  its  varieties  are  easily  recognized. 

It  is  sufficiently  hard  to  scratch  glass,  and  it  always  gives  sparks 
with  steel.  When  pure,  its  specific  gravity  is  about  2.  63.  water 
being  1.  ;  but  in  certain  varieties  extends  above  and  below  this 
term,  depending  on  its  structure,  or  the  presence  of  foreign  ingre- 
dients. Indeed,  the  mean  specific  gravity  of  the  whole  species,  is 
about  2.  60.  It  is  sometimes  in  amorphous  masses,  and  sometimes 
in  very  beautiful  crystals,  of  which  the  primitive  form  is  a  rhomb 
slightly  obtuse,  the  angles  of  its  faces  being  94°  24'  and  85°  36'. — 
The  secondary  form,  the  most  common,  is  a  six-sided  prism,  termi- 
nated by  six-sided  pyramids.  It  exhibits  double  refraction,  which 
must  be  observed  by  viewing  an  object  through  one  face  of  the  pyr- 
amid and  the  opposite  side  of  the  prism.    Its  fracture  is  vitreous. 

(Chemical  Characters.)  All  the  varieties  of  quartz  are  infusible 
by  the  blow-pipe,  and  if  pure,  it  is  scarcely  softened,  even  when 
the  flame  is  excited  by  oxygen  gas.  Before  the  compound  blow-pipe, 
a  fragment  of  rock  chrystal  instantly  melts  into  a  white  glass. — 
Quartz  is  essentially  composed  of  silex  or  the  principal  ingredient 
of  flint,  from  93  to  98  parts  being  of  this  substance,  and  the  residue 
alumine,  lime,  water,  or  some  metallic  oxide. 

Among  the  varieties,  are  1.  the  Limpid  Quartz,  (Rock  Crystal,) — 
This,  the  most  perfect  variety  of  Quartz,  has,  when  crystalized,  re- 
ceived the  name  of  rock  crystal ;  indeed  the  same  name  is  sometimes 
extended  to  colored  crystals,  when  transparent.  Limpid  quartz  is 
without  color,  and  sometimes  as  transparent  as  the  most  perfect 
glass,  which  it  strongly  resembles.  It  is,  however,  harder  than  glass, 
and  the  flaws  or  bubbles,  which  it  often  contains,  lie  in  the  same 
plane,  while  those  in  glass  are  irregularly  scattered.  The  finest  crys- 
tals are  found  in  veins,  or  cavities,  in  primitive  rocks,  as  in  granite, 
gneiss  or  mica  slate,  or  in  alluvial  earths. 

In  the  United  States  this  variety  is  not  uncommon.  It  is  found  in 
Virginia,  near  the  North  Mountain.  In  Frederick  Co.  Maryland, 
crystals  are  scattered  on  the  surface  of  the  ground,  of  perfect  trans- 
parency, with  a  splendent  lustre.  In  New-York,  on  an  island  in  Lake 
George,  are  very  fine  crystals — and  in  Vermont,  at  Grafton.  This 
variety  is  sometimes  employed  in  Jewelry,  for  watch  seals,  fyc. 

2.  Smoky  Quartz.  Objects  seen  through  this  variety,  seem  to  be 
viewed  through  a  cloud  of  smoke.  Its  true  color  seems  to  be  clove 
brown.    It  is  sometimes  called  smoky  topaz. 

3.  Yellow  Quartz.  Its  color  is  pale  yellow,  sometimes  honey  or 
straw  yellow.  It  has  been  called  citrine  ;  and  also  false,  or  Bohemi- 
an topaz. 

4.  Blue  Quartz.  Its  color  is  blue,  or  grayish  blue.  It  is  inferior 
in  hardness  to  the  former  varieties. 

5.  Rose  Red  Quartz.  Its  color  is  rose  red  of  different  shades, 
sometimes  with  a  tinge  of  yellow.    It  is  seldom  more  than  semi- 


OF  GRANITE. 


19 


transparent.  Its  color,  which  is  supposed  to  arise  from  manganese, 
is  said  to  be  injured  by  exposure  to  light,  It  has  been  called  Bohe- 
mian ruby.   It  is  sometimes  employed  in  jewelry,  and  much  esteemed. 

6.  Irised  Quartz.  It  reflects  a  series  of  colors,  similar  to  those  of 
the  iris  or  rainbow. 

7.  Aventurine  Quartz.  Its  predominant  color,  which  may  be  red, 
yellow,  gray,  greenish,  blackish,  or  even  white,  is  variegated  by 
brilliant  points,  which  shine  with  silver  or  golden  lustre.  It  is 
sometimes  employed  in  ornaments  of  jewelry. 

8.  J\Tilky  Quartz.  Its  color  is  milk  white,  in  some  cases  a  little 
bluish  ;  and  it  is  nearly  opaque.  Its  fracture  has  sometimes  a  res- 
inous lustre.  It  is  sometimes  in  small  crystals,  but  more  often  in 
large  masses. 

9.  Greasy  Quartz.  Its  colors  are  various,  either  light  or  dark. 
Its  fracture  appears  as  if  rubbed  with  oil. 

10.  Radiated  Quartz.  It  is  in  masses  which  have  a  crystalline 
structure,  and  are  composed  of  imperfect  prisms.  These  prisms 
usually  diverge  a  little,  or  radiate  from  the  centre,  and  often  sepa- 
rate with  great  ease. 

1 1 .  Tabular  Quartz.  It  occurs  in  plates  of  various  sizes,  which 
are  sometimes  applied  to  each  other  by  the  broader  faces. 

12.  Granular  Quartz.  Its  structure  presents  small  granular  con- 
cretions, or  grains,  which  are  sometimes  feebly  united.  This  varie- 
ty must  be  carefully  distinguished  from  certain  sand-stones  which  it 
resembles.  It  may  be  important — in  the  manufacture  of  glass,  and 
certain  kinds  of  stone-ware. 

13.  Arenaceous  Quartz.  It  is  in  loose  grains,  coarse  or  fine,  either 
angular  or  rounded,  and  constitutes  some  varieties  of  pure  sand. — 
Certain  sand-stones  appear  to  be  composed  of  this  quartz,  united  by 
some  cement. 

14.  Pseudomorphous  Quartz.  It  appears  under  regular  forms,  such 
as  cubes,  octaedrons,  &c.  which  do  not  belong  to  the  species.  They 
are  opaque,  their  surfaces  dull,  and  their  edges  often  blunted. 

Common  quartz  never  forms  whole  mountains.  It  is  sometimes 
in  large  masses,  or  in  beds,  and  frequently,  in  extremely  large  veins, 
which  have  been  mistaken  for  beds.  Quartz,  in  the  form  of  crys- 
talized  grains,  or  of  irregular  masses  of  various  sizes,  is  abundantly 
disseminated  in  granite,  gneiss,  mica  slate,  &c.  of  all  which  it  forms 
a  constituent  part.  It  is  sometimes  in  regular  crystals,  dispersed 
through  the  granite.  In  porphyry,  also,  it  is  sometimes  regularly 
crystalized.  It  also  occurs  in  carbonate  of  lime,  anthracite,  fyc. — 
Among  secondary  rocks,  quartz  is  found  forming  a  greater  part  of 
many  sand-stones  ;  also  between  strata  of  compact  limestone,  of  clay, 
or  of  marl,  or  imbedded  in  sulphate  of  lime. 

In  alluvial  earths  it  exists  in  the  form  of  sand.  Quartz  is  often 
associated  with  the  carbonate  and  fluate  of  lime,  sulphate  of 
barytes,  and  feldspar,  in  metallic  veins  ;  indeed,  it  exists  in  almost 
every  metallic  vein. 


20 


OPERATIVE  MASONRY. 


Hornblend,  schorl,  epidote,  garnet,  magnetic-iron,  are  also  among 
the  minerals  contained  in  quartz.    Mica  gives  it  a  slaty  structure. 

In  some  rare  instances,  bubbles  of  air,  and  even  drops  of  water, 
and  bitumen,  have  been  found  in  quartz.  Although  common  quartz 
never  contains  any  organic  remains,  it  is  sometimes  crystalized  in 
fossil  wood. 

Quartz  is  found  very  abundantly  in  most  of  the  northern  and 
middle  states. 

We  have  already  seen  that  certain  varieties  of  quartz  are  employed 
in  Jewelry.  It  is  also  used,  especially  the  sandy  variety,  in  the  man- 
ufacture of  glass  ;  also  in  the  preparation  of  smalt  and  certain 
enamels. 

II.  Feldspar.  This  important  and  widely  distributed  mineral, 
has,  in  most  of  its  varieties,  a  structure  very  distinctly  foliated.  It 
scratches  glass,  and  gives  sparks  with  steel,  but  its  hardness  is  a  little 
inferior  to  that  of  quartz.  When  in  crystals  or  crystaline  masses, 
it  is  very  susceptible  of  mechanical  division,  at  natural  joints,  which, 
in  two  directions  perpendicular  to  each  other,  are  extremely,  per- 
fect ;  but  in  the  third  direction,  they  are  usually  indistinct. 

The  primitive  form,  thus  obtained,  is  an  oblique,  angled  parallelo- 
gram, whose  sides  are  inclined  to  each  other  in  angles  of  90° 
120°  and  111°  28'.  The  four  sides,  produced  by  the  two  divisions, 
perpendicular  to  each  other,  have  a  brilliant  polish,  while  the  two 
other  sides  are  dull  ;  this  is  a  distinctive  character  of  great  impor- 
tance. Its  specific  gravity  usually  lies  between  2.  43  and  2.  70. — 
It  possesses  double  refraction,  which,  however,  is  not  easily  obser- 
ved.   It  is  usually  phosphorescent,  by  friction,  in  the  dark. 

(Chemical  Characters.)  Before  the  blow-pipe  it  melts  into  a  white 
enamel  or  glass,  more  or  less  translucent.  The  results  of  analysis 
have  not  yet  been  perfectly  satisfactory  in  regard  to  the  true  com- 
position of  feldspar.  It  appears  probable,  however,  that  not  only 
silex  and  aluinine,  but  also  lime  and  potash  are  essential  ingredients. 
In  a  specimen  of  green  feldspar  Vauquebin  found  62.  83  parts  of 
silex,  17.  02  of  alumine,  13.  0  of  potash,  3.  0  of  lime,  and  1.  0  of 
oxide  of  iron  —  96.  85  in  an  100  parts. 

Several  of  the  varieties  of  Feldspar  deserve  notice. 

1.  Common  Feldspar.  This  variety  occurs  in  fragments  often 
rolled,  also  in  grains  in  sand,  but  more  commonly  in  masses  of  mod- 
erate size,  forming  an  ingredient  of  compound  minerals.  It  is  not 
unfrequently  in  regular  crystals,  of  the  primitive  form,  already 
mentioned. 

The  crystals  of  feldspar,  seldom  very  small,  are  sometimes  several 
inches  both  in  diameter  and  length  ;  their  faces  are  shining,  and 
their  edges  sometimes  very  perfect.  Their  prevailing  form  is  an 
oblique  prism,  whose  sides  are  unequal,  and  vary  in  number,  from 
four  to  ten.  The  terminating  faces,  of  which  two  are  commonly 
longer  than  the  others,  are  subject  to  great  variation  in  number  and 
extent ;  indeed,  they  often  seem  to  have  no  symmetry  in  their  ar- 
rangement, a  circumstance  which  arises  from  the  obliquity  and 
irregularity  of  the  primitive  form. 


OF  GRANITE. 


21 


The  longitudinal  fracture  is  foliated,  and  its  lustre  more  or  less 
shining  and  vitreous,  sometimes  pearly}  especially  in  certain  spots; 
the  cross  fracture  is  uneven  or  splintery,  and  nearly  dull.  It  is 
easily  broken,  and  falls  into  rhomboidal  fragments,  which  have 
four  polished  faces.  The  folia  are  sometimes  curved,  or  arranged 
like  the  petals  of  a  flower. 

It  is  more  or  less  translucent,  sometimes  nearly,  or  quite  opaque, 
and  presents  a  great  variety  of  colors.  Among  these  are  white, 
tinged  with  gray,  yellow,  green  or  red  ;  gray,  often  with  a  shade 
of  blue  ;  several  shades  of  red,  as  flesh  or  blood  red  ;  to  which  must 
be  added  green,  yellow,  brown,  or  even  black. 

This  variety  is  abundant,  and  constitutes  an  essential  ingredient 
of  granite,  gneiss,  sienite,  and  green-stone.  Of  granite  and  sienite 
it  sometimes  forms  two  thirds  of  the  whole  mass.  It  exists  also  in 
argillite  and  porphyry  &c.  Its  crystals,  though  sometimes  imbed- 
ded, are  more  often  found  in  the  fissures  or  cavities  of  these  rocks, 
and  are  sometimes  associated  with  epidote,  axinite,  chronite,  amian- 
thus, carbonate  of  lime,  quartz,  magnetic  oxide  of  iron  &c. 

2.  Green  Feldspar.  The  variety  is  rare,  and  has  an  apple-green 
color,  varying  somewhat  in  intensity,  and  sometimes  marked  with 
whitish  stripes. 

3.  Adularia.  This  is  the  most  perfect  variety  of  feldspar,  and  bears 
to  common  feldspar,  in  many  respects,  the  relation  of  rock  crys- 
tal to  common  quartz.  It  is  more  or  less  translucent,  and  sometime 
transparent  and  limpid.  Its  color  is  white,  either  a  little  milky, 
or  with  a  tinge  of  green,  yellow,  or  red.  But  it  is  chiefly  distin- 
guished by  presenting,  when  in  certain  positions,  whitish  reflections, 
which  are  often  slightly  tinged  with  blue  or  green,  and  exhibit  a 
pearly  or  silver  lustre.  Adularia  is  sometimes  cut  into  plates  and 
polished.  The  fah*s  eye  moon-stone,  and  argentine  of  lapidaries  come 
chiefly  from  Persia,  Arabia,  and  Ceylon,  and  belong  to  Adularia, 
as  do  also  the  water-opal  and  girasole  of  the  Italians. 

4.  Opalescent  Feldspar.  This  very  beautiful  variety  is  distinguish- 
ed by  its  property  of  reflecting  light  of  different  colors,  which  ap- 
pear to  proceed  from  its  interior.  Its  proper  color  is  gray,  often 
dark  or  blackish  gray,  and  sometimes  specimens  are  marked  with 
whitish  spots  or  veins.  But  when  held  in  certain  positions  it  reflects 
a  very  lively  and  beautiful  play  of  colors,  embracing  almost  every 
shade  of  green  and  blue,  and  several  shades  of  yellow,  red,  gray, 
and  brown.  These  colors  are  usually  confined  to  certain  spots,  and 
even  the  same  spot  changes  its  color  in  different  positions.  It  is 
much  esteemed  in  jewelry. 

5.  Jlventurine  Feldspar.  Its  colors  are  various  ;  but  it  contains 
little  spangles  or  points,  which  reflect  a  brilliant  light. 

6.  Petuntze.  It  is  nearly,  or  quite  opaque,  and  its  color  is  usually 
whitish  or  gray.  It  has,  in  most  cases,  less  lustre  than  common 
feldspar.  It  most  usually  occurs  in  beds.  Its  powder  is  said  to 
have  a  slightly  saline  taste.  It  is  used  in  the  manufacture  of  porce- 
lain, both  for  an  enamel,  and  its  composition* 


22 


OPERATIVE  MASONRY. 


7.  Granular  Feldspar.  It  is  nearly,  or  quite  opaque,  and  imper- 
fectly foliated.  It  varies  much  in  hardness,  and  is  sometimes  friable 
between  the  fingers.  Its  color  is  usually  white,  and  sometimes 
strongly  resembles  masses  of  white  sugar.  Feldspar  is  found  in  the 
northern,  and  most  of  the  middle  states. 

III.  Mica.  Mica  appears  to  be  always  the  result  of  crystaliza- 
tion,  but  it  is  rarely  found  in  regular,  well  defined  crystals.  Most 
commonly  it  appears  in  thin,  flexible,  elastic  laminae,  which  exhibit 
a  high  polish  and  strong  lustre.  These  laminae  have  sometimes  an 
extent  of  many  square  inches  ;  and  from  this,  gradually  diminish, 
till  they  become  mere  spangles.  They  are  usually  found  united 
into  small  masses,  extremely  variable  in  thickness,  or  into  crystals 
more  or  less  regular  ;  their  union,  however,  is  so  very  feeble,  that 
they  are  easily  separable,  and  may  be  reduced  to  a  surprising  de- 
gree of  tenuity.  In  this  state  their  surface  becomes  irised,  and  their 
thickness  does  not  exceed  a  millionth  part  of  an  inch. 

The  crystals  of  mica  are  sometimes  right  prisms  with  rhombic 
bases,  whose  angles  are  120°  and  62°.  This  is  also  the  primitive 
form,  in  which  one  side  of  the  base  is,  to  the  height  of  the  prism, 
nearly  as  3  to  8. 

The  structure  of  Mica  is  always  foliated,  but  the  foliae  may  be 
straight,  curved  or  undulated.  The  surface  has  a  shining  or 
splendent  lustre,  which  is  usually  metallic,  sometimes  like  that  of 
silver  or  gold  ;  and  sometimes  like  that  of  polished  glass.  It  is 
easily  scratched  by  a  knife,  and  in  most  cases,  even  by  the  finger 
nail.  Its  surface  is  smooth  to  the  touch,  and  very  seldom  slightly 
unctuous  ;  its  powder  is  dull,  grayish,  and  feels  soft.  It  is  often 
transparent,  in  other  cases  it  is  only  translucent,  sometimes  at  the 
edges  only.  Its  colors  are  silver  white,  grey,  often  tinged  with 
yellow,  green,  or  black  ;  also  brown,  reddish,  and  green. 

Its  specific  gravity  extends  from  2.53  to  2.93  ;  and  when  rubbed 
on  sealing  wax,  it  communicates  to  the  wax  negative  electricity. 

[Chemical  Characters.)  It  is  fusible  by  the  blow-pipe,  though  some- 
times with  difficulty,  into  enamel,  which  is  usually  gray  or  black. 
The  colored  varieties  are  the  most  easily  fusible  ;  and  black  mica 
gives  a  black  enamel,  which  often  moves  the  needle.  It  contains, 
according  to  Klaproth,  silex  48.0,  alumine  34.25,  potash  8.75,  oxide 
of  iron,  4.5,  oxide  of  manganese  0.5  ;=96.  Sometimes  the  potash  is 
in  greater  proportion,  and  in  black  mica  the  oxide  of  iron  is  some- 
times as  high  as  22  per  cent.  Mica  is  subject  to  decomposition  by 
exposure  to  the  atmosphere. 

The  following  are  the  most  important  varieties  of  mica. 

1.  Laminated  Mica.  It  occurs  in  large  plates,  which  often  contain 
many  square  inches.  It  has  been  called  Muscovy  glass,  or  talc,  being 
found  abundantly  in  that  country. 

2.  Lamellar  Mica.  This  is  the  more  common  variety.  It  exists 
in  small  foliae,  either  collected  into  masses,  or  disseminated  in  other 
minerals.  It  is  sometimes  in  extremely  minute  scales,  which,  when 
detached  from  the  mass,  appear  like  sand. 


OF  GRANITE. 


23 


3.  Prismatic  Mica.  This  variety  is  not  common.  The  laminae 
are  easily  divisible,  parallel  to  their  edges,  into  minute  prisms,  or 
even  into  delicate  filaments.  The  edges  of  the  laminae  have  usually 
more  lustre  than  those  of  the  other  varieties. 

Although  mica  never  occurs  in  beds,  or  large  insulated  masses, 
there  is  no  substance  more  universally  diffused  through  the  mineral 
kingdom.  It  is  an  essential  ingredient  in  granite,  gneiss,  and 
mica-slate  ;  and  occurs  also  in  sienite,  porphyry,  and  other  primi- 
tive rocks.  Mica  occurs  also  in  green-stone,  basalt,  sand-stone,  and 
other  secondary  rocks;  especially  in  sand-stone  and  shell,  which  ac- 
company coal, 

In  the  United  States  mica  is  very  abundant. 

It  has  been  employed  instead  of  glass,  in  the  windows  of  dwelling 
houses;  also  in  ships  of  war,  because  it  is  not  liable  to  be  broken  by 
the  concussion  produced  by  the  discharge  of  cannon.  In  lanterns 
it  is  superior  to  horn,  being  more  transparent,  and  not  so  easily  in- 
jured by  heat.  When  in  thin  transparent  laminae,  sufficiently 
large,  it  is  useful  to  defend  the  eyes  of  those  who  travel  against 
high  winds  and  severe  storms  of  snow.  When  of  suitable  color  and 
in  minute  scales,  it  is  employed  to  ornament  paper,  which  is  then 
said  to  he  frosted;  the  scales  of  mica  are  made  to  adhere  by  a  solution 
of  gum  or  glue. 

These  are  the  ingredients,  of  which  granite  is  composed. 

The  structure  of  granite  is  granular;  but  the  grains  are  extremely 
variable  both  in  size  and  form.  Most  frequently  the  size  of  the 
grains  lies  between  that  of  a  pin's  head  and  a  nut.  Sometimes, 
however,  they  are  several  inches,  and  even  more  than  a  foot,  in  their 
dimensions,  and  sometimes  they  are  so  minute,  that  the  mass  re- 
sembles a  sand-stone,  or  even  appears  almost  homogeneous  to  the 
naked  eye. 

The  forms  of  these  grains  are,  in  general,  altogether  irregular,  like 
those  of  the  fragments  of  most  minerals.  In  some  granites  the  feldspar 
or  quartz,  or  even  the  mica,  is  in  crystals  more  or  less  regular. 

The  ingredients  of  granite  vary  much  in  their  proportions;  but  in 
general,  the  feldspar  is  most  abundant,  and  the  mica  is  usually  in  the 
smallest  proportion.  Their  arrangement  is  also  various;  sometimes, 
while  the  feldspar  and  quartz  are  mingled  with  considerable  uniform- 
ity, the  mica  appears  only  in  scattered  masses,  or  is  found  investing 
grains  of  feldspar  and  quartz  on  all  sides.  In  other  cases  the  felds- 
par and  mica,  or  quarts  and  mica  are  mingled,  while  the  third  in- 
gredient appears  in  small  distinct  masses. 

One  of  the  ingredients  of  this  rock,  most  frequently  the  quartz  or 
mica,  may  be  entirely  wanting,  through  a  greater  or  less  portion  of 
the  mass,  so  that  specimens  of  true  granite,  (as  it  is  sometimes  called) 
contain  only  two  ingredients. 

The  predominant  color  of  granite  usually  depends  on  that  of  the 
feldspar,  which  may  be  white  or  grey,  sometimes  with  a  shade  of 
red,  yellow,  blue,  or  green,  and  sometimes  it  is  flesh  red.  The 
quartz  may  be  white,  grayish- white,  or  grey,  sometimes  very  dark; 
but  it  is  usually  vitreous  and  translucent.  The  mica  may  be  black, 
brown,  grey,  silver,  white,  yellowish  or  violet. 
4 


24 


OPERATIVE  MASONRY. 


The  simple  minerals,  which  enter  into  the  composition  of  granite, 
are,  in  general,  so  intimately  united,  that  the  mass  is  firm  and  solid; 
but  some  varieties  are  brittle,  and  easily  become  disintegrated. 
The  feldspar  sometimes  undergoes  a  partial  decomposition,  losing 
its  lustre,  hardness,  and  foliated  structure,  while,  at  other  times,  it 
is  converted  into  porcelain  clay.  The  mica  also,  when  exposed  to 
the  open  air,  is  subject  to  alteration,  or  even  decomposition.  Sul- 
phuric acid  is  often  generated  by  the  decomposition  of  the  Sulphuret 
of  iron,  disseminated  in  the  granite,  and  this  acid  acts  upon  the  mica 
in  its  vicinity,  thus  producing  a  soft  substance,  and  diminishing  the 
firmness  of  the  granite.  Grange,  which  embraces  schorl,  is  also 
liable  to  disintegration. 

The  specific  gravity  of  granite  general  lies  between  2.  5  and  2. 
6,  but  is  sometimes  higher. 

Among  the  varieties  of  granite  are, 

1.  Graphic  Granite.  This  very  beautiful  variety  of  granite  is 
composed  chiefly  of  feldspar  and  quartz.  The  feldspar  is  very  abun- 
dant, forming  a  base,  in  which  quartz,  under  various  forms,  lies  im- 
bedded. When  this  granite  is  broken  in  a  direction,  perpendicular 
to  that  in  which  the  quartz  traverses  the  feldspar,  the  surface  of 
the  fracture  ordinarily  presents  the  general  aspect  of  letters,  arranged 
in  parallel  lines  ;  and  hence  its  name.  These  letters  of  grey,  vit- 
reous quartz,  on  a  shining  and  polished  tablet  of  white,  or  flesh 
colored  feldspar,  appear  extremely  beautiful.  It  is  principally  this 
variety  of  granite,  which,  by  its  decomposition,  furnishes  porcelain 
clay. 

2.  Globular  Granite.  This  is  composed  of  large,  globular,  dis- 
tinct concretions,  which  are  sometimes  several  feet  in  diameter. 
These  concretions  are  united  by  a  kind  of  granite,  which  is  readily 
disintegrated,  thus  leaving  the  globular  masses  detached  from  each 
other. 

3.  Porphyritic  Granite.  This  variety  is  produced,  when  large 
crystals  of  feldspar  are  interspersed  in  a  fine-grained  granite. 

Granite  is  always  a  primitive  rock  ;  and  never  embraces  any  or- 
ganic remains  of  animals  or  vegetables. 

It  exists  very  extensively,  and  in  many  countries  it  occurs  in  im- 
mense quantities.  It  constitutes  a  large  portion  of  many  of  the 
highest  mountains,  of  which  it  appears  to  form  the  central  parts,  as 
well  as  the  summits.  It  is  more  or  less  abundant  in  the  mountains 
of  Scotland  and  Germany  ;  the  Alps,  the  Carpathean,  the  Uralian, 
and  the  Altian  mountains ;  the  Andes,  and  the  United  States. 

Granite  is  chiefly  used  as  a  building  stone.  It  is  split  from  the 
quarries  by  rows  of  iron  wedges,  driven  simultaneously  in  the  di- 
rection of  the  intended  fissure.  This  method  is  thought  by  Brard 
to  have  been  known  to  the  ancient  Romans  and  Egyptians.  The 
blocks  are  afterwards  hewn  to  a  plane  surface,  by  the  strokes  of  a 
sharp-edged  hammer.  Granite  is  also  chisseled  into  capitals  and 
decorative  objects,  but  this  operation  is  difficult,  owing  to  its  hard- 
ness and  brittleness.  It  is  polished  by  long-continued  friction,  with 
sand  and  emery. 


OF  SIEN1TE. 


35 


The  largest  mass  of  granite,  known  to  have  been  transported  in 
modern  times,  is  the  pedestal  of  the  equestrian  statue  of  Peter  the 
Great,  at  St.  Petersburg.  It  is  computed  to  weigh  three  millions 
pounds,  and  was  transported  nine  leagues,  by  rolling  it  on  cannon 
balls  :  those  of  iron  being  crushed,  others  of  bronze  were  substi- 
tuted. Sixty  granite  columns  at  St.  Petersburg,  consist  each  of  a 
single  stone,  twenty  feet  high.  The  columns  in  the  portico  of  the 
Pantheon  at  Rome,  which  are  thirty-six  feet,  eight  inches  high,  are 
also  of  granite.  The  shaft  of  Pompey's  Pillar,  in  Egypt,  is  sixty- 
three  feet  in  height,  and  of  a  single  piece.  It  is  said  to  be  of  red- 
granite,  but  is  possibly  sienite.  In  the  Eastern  part  of  the  United 
States,  a  beautiful  white  granite  is  found  in  various  places,  and  is 
now  introduced  into  building.  The  new  Market-House  in  Boston, 
the  United  States  Bank,  the  Tremont  House  and  Theatre,  &c.  are 
made  of  it. 


SECTION  VI.  SIENITE. 

This  rock  is  related  to  Granite,  and  resembles  it  in  its  general 
characters.  Feldspar  and  hornblend  may  be  considered  its  constant 
and  essential  ingredients.  Feldspar  is  the  most  abundant  ingredi- 
ent, and  has  already  been  described,  (see  granite)  but  as  it  is,  how- 
ever, the  presence  of  hornblend,  as  a  constituent  part,  which 
distinguishes  this  rock  from  granite,  some  account  of  it  may  be 
useful. 

I.  Hornblend  is  a  very  common  mineral,  and  may,  in  general, 
be  easily  recognized.  Sometimes  it  is  in  regular  and  distinct  crys- 
tals, but  more  commonly  it  appears  in  masses,  composed  of  laminae, 
or  fibres,  variously  aggregated,  the  result  of  confused  crystalliza- 
tion. 

When  its  structure  is  sufficiently  regular,  mechanical  division  is 
easily  effected  in  a  longitudinal  direction  ;  and  its  crystals  are  found 
to  be  composed  of  laminae,  situated  parallel  to  the  sides  of  an  ob- 
lique four-sided  prism,  with  rhombic  bases  ;  the  sides  of  this  prism 
are  inclined  to  each  other,  at  angles  of  124°  34'  and  55D  26'.  The 
longitudinal  fracture  is  of  course  foliated,  and  usually  presents  the 
broken  edges  of  many  laminae  extending  one  beyond  another. 

Hornblend  usually  scratches  glass,  and  sometimes  with  difficulty 
gives  sparks  with  steel.  Its  powder  is  dry,  and  not  soft  to  the 
touch.  It  is  often  opaque,  sometimes  translucent.  It  is  generally 
black  and  green,  often  intermixed.  Its  specific  gravity  is 
about  3.  20. 

[Chemical  Characters.)  Before  the  blow-pipe  it  melts  with  con- 
siderable ease,  and  forms  black,  or  greyish  black  glass,  or  greyish 
enamel.  It  yields,  by  analysis,  silex,  alumine,  magnesia,  and  lime, 
but  in  variable  proportions.  Its  colors  are  produced  by  the  oxides 
of  iron  and  of  chrome. 


26 


OPERATIVE  MASONRY. 


Masses  of  hornblend,  whether  fibrous,  lamellar,  or  nearly  com- 
pact, possess  a  remarkable  tenacity,  which  renders  them  tough  and 
difficult  to  break  ;  indeed,  a  considerable  cavity  may  often  be  produ- 
ced by  the  hammer,  before  the  mass  breaks.  They  exhale  when 
moistened  by  the  breath,  a  peculiar  argillaceous  odor. 

Some  of  the  varieties  are, 

1.  Basaltic  Hornblende  which  is  found  in  lava  and  volcanic 
scoriae,  and  very  often  in  Basalt ;  and  hence  its  name.    It  is  almost 

.  always  in  distinct  crystals,  whose  color  is  a  pure  black,  sometimes 
slightly  tinged  with  green,  or  brownish,  by  decomposition.  Their 
surface  is  sometimes  strongly  shining,  at  other  times  dull,  and  in- 
vested with  a  feruginous  crust.  Its  structure  is  more  foliated,  than 
that  of  other  varieties,  and  its  crystals  more  brittle. 

2.  Lamellar  Hornblend.  Its  masses  are  sometimes  composed 
merely  of  lamellar,  and  sometimes  of  granular  concretions  of  various 
sizes,  having  a  lamellated  structure.  Hence  the  fracture  is  foliated, 
but  the  foliae  are  variously  inclined  and  interlaced. 

3.  Fibrous  Hornblend.  It  occurs  in  masses,  composed  of  acicular 
crystals  or  fibres,  either  broad  or  narrow,  parallel  or  interlaced. 

4.  Slaty  Hornblend  or  Hornblend  Slate.  This  variety  scarcely 
differs  from  the  preceding,  except  in  the  slaty  structure  of  its  mass- 
es. For  each  individual  layer  is  composed  of  very  minute  fibres, 
diverging  in  bundles,  or  promiscuously,  and  often  interlaced. 

Hornblend  is  an  essential  ingredient  in  sienite  and  green-stone,  as 
well  as  in  basalt  and  lava. 

Sienite,  being  composed  of  these  two  ingredients,  is  usually  gran- 
ular ;  but  the  grains  are  sometimes  coarse,  and  sometimes  very  fine. 
In  some  instances  its  structure  is  slaty.  When  this  rock  is  very  fine 
grained,  and,  at  the  same  time,  contains  large  crystals  of  feldspar, 
it  constitutes  sienetic  porphyry. 

The  feldspar,  whose  foliated  texture  is  often  very  distinct,  is  most 
frequently  reddish  or  whitish  ;  but  sometimes  it  receives  a  greenish 
tinge,  from  the  hornblend,  or  from  epidote. 

Sienite  is  sometimes  found  resting  on  granite,  gneiss,  mica-slate, 
or  argillite,  and  sometimes  it  is  associated  with  green-stone  and  ar- 
gillaceous porphyries. 

This  rock  is  often  altered  at  the  surface  by  the  action  of  the 
weather,  more  especially  in  those  varieties,  which  contain  an  un- 
common proportion  of  feldspar.  It  often  is  susceptible  of  a  good 
polish  ;  and  may  be  employed  for  the  same  purposes  as  porphyry. 
Its  name  is  derived  from  that  of  Sienna,  a  city  in  Egypt,  where  it  is 
found  in  abundance,  and  constitutes  the  material  of  many  of  the 
obelisks.  The  Romans  imported  it  for  purposes  of  statuary  and 
architecture. 

Sienite  is  obtained  in  large  pieces,  and  possesses  all  the  valuable 
qualities  of  granite,  as  a  building  stone.  It  is  somewhat  harder  than 
granite,  and  more  difficult  to  chissel.  It  is  found  abundantly,  near 
Boston,  at  Weymouth,  Brighton,  Quincy,  &c.  and  is  introduced 
into  many  structures.    The  Washington  Bank,  and  the  Bunker  Hill 


OF  GREEN-STONE. 


27 


monument  consist  of  this  stone.  It  is  rendered,  by  its  extreme  hard- 
ness, one  of  the  best  materials  for  M'Adamising  roads.  The  rail- 
way at  Quincy,  is  built  for  transporting  this  stone  from  the  quarry 
to  the  sea,  and  it  is  there  commonly  called  the  Quincy  stone. 


SECTION  VII.  Green-Stone. 

4 

Sienite  and  green-stone  are  essentially  composed  of  the  same  in- 
gredients, namely,  feldspar  and  hornblend.  And  the  two  rocks  do, 
in  fact,  pass  into  each  other  by  insensible  shades.  But  in  greenstone,  the 
hornblend  predominates,  while,  in  sienite,  the  feldspar  is  the  most  abun- 
dant ingredient.  This  frequently  gives  to  this  stone,  more  or  less 
of  a  greenish  tinge,  especially  when  it  is  moistened  ;  hence  the  name 
of  this  rock.  Sometimes  the  tinge  of  green  is  considerable  lively  ; 
sometimes,  also,  its  color  is  a  dark  gray,  or  grayish  black.  In  short, 
its  color,  especially  at  the  surface,  is  often  modified  by  the  pres- 
ence of  oxide  of  iron. 

It  presents  a  considerable  diversity  of  aspect,  depending  on  the 
general  structure,  or  on  the  size,  proportion,  disposition,  and  more 
or  less  intimate  mixture  of  its  constituent  parts.  From  green-stone, 
with  a  coarse  granular  structure,  to  those  varieties  whose  texture  is 
so  finely  granular  that  the  two  ingredients  can  scarcely  be  per- 
ceived, there  is  a  gradual  passage,  exhibiting  every  intermediate 
step.  Indeed,  the  grains  are  sometimes  so  minute,  and  so  uniformly 
and  intimately  mingled,  that  the  mass  appears  altogether  homoge- 
neous, and  the  different  ingredients  are  hardly  perceptible — even 
with  a  glass. 

It  sometimes  presents  prisms  or  columns  of  various  size.  These 
prisms  may  have  from  three  to  seven  sides,  and  are  often  quite  regu- 
lar. Many  green-stones  are  susceptible  of  a  polish.  It  occurs  in 
beds,  more  or  less  large,  and  sometimes  forms  whole  mountains. 

Green-stone  is  common  in  the  United  States.  When  this  rock 
breaks  into  prismatic  fragments,  it  forms  a  very  useful  building 
stone.  Most  of  its  varieties,  when  heated  red  hot,  plunged  into 
cold  water,  and  pulverized,  become  a  good  substitute  for  puzzolana 
in  preparing  water-proof  mortar  for  the  construction  of  walls,  cel- 
lars, docks,  piers,  &c.  This  rock  has  sometimes  received  the  ap- 
pellation of  Trap,  which  seems  to  be  a  generic  term,  applied  to 
those  stones,  which  consist  principally  of  hornblend. 


SECTION  VIII.  Sand-Stone  or  Free-Stone. 

Sand-stone  is  composed,  generally,  of  grains  of  quartz,  (see  granite) 
united  by  a  cement,  which  is  never  very  abundant,  and  often,  in- 
deed, nearly  or  quite  invisible.  These  grains  are  sometimes  scarcely 
distinguishable  by  the  naked  eye,  and  sometimes  their  magnitude  is 
equal  to  that  of  a  nut  or  an  egg. 


28 


OPERATIVE  MASONRY. 


The  cement  is  variable  in  quantity,  and  may  be  calcareous  or 
merely  argillaceous,  or  siliceous.  When  siliceous,  the  mineral  much 
resembles  quartz.  The  texture  of  some  sand-stones  is  very  close, 
while  that  of  others  is  so  loose  and  porous,  as  to  permit  the  passage 
of  water. 

Some  varieties  are  sufficiently  hard  to  give  fire  with  steel,  while 
others  are  friable,  and  may  be  reduced  to  powder,  even  by  the 
fingers  ;  this  is  often  the  case  with  those  sand-stones  whose  cement 
is  marly. 

Its  fracture  is  always  granular  or  earthy  ;  in  some  instances  it 
may,  at  the  same  time,  be  splintery.  Some  sand-stones  have  a  slaty 
structure,  arising  from  scattered  plates  of  mica,  and  have  been  called 
sand-stone  slate. 

Its  most  common  color  is  gray  or  grayish,  it  is  sometimes  redish, 
or  redish  brown.  In  some  cases  the  color  is  uniform,  in  others 
variegated. 

Among  the  varieties  are, 

1.  Red  Sand- Stone.  The  grains  of  this  variety  are  usually  coarse, 
and  united  by  an  argillaceous  cement,  which  is  at  the  same  time 
feruginous ;  hence  the  dark  redish,  or  redish  brown  color,  which 
it  presents. 

2.  Variegated  Sand- Stone.  This  presents  a  variety  of  colors  ;  as 
yellow,  green,  brown,  red,  and  white,  which  are  usually  arranged 
in  stripes,  or  zones,  either  straight  or  wavering.  It  has  commonly  a 
close  texture  and  fine  grain  ;  but  it  very  often  embraces  roundish 
masses  of  clay,  which  often  fall  out  when  exposed  to  the  weather, 
and  diminish  its  value  for  the  purposes  of  architecture. 

3.  White  Sand- Stone.  This  includes  many  of  the  more  common 
and  valuable  varieties  of  sand-stone.  Its  color  is  whitish  gray,  or 
gray,  and  generally  uniform  ;  but  sometimes  it  is  marked  with  red- 
ish spots.  Its  cement  is  often  calcareous.  .  It  is  well  adapted  for 
various  uses  in  the  arts. 

Sand-stone  is,  in  general,  more  or  less  distinctly  stratified.  Its 
beds  are  very  often  nearly  or  quite  horizontal  ;  but  sometimes,  es- 
pecially in  the  older  varieties,  they  are  much  inclined,  or  even  ver- 
tical. Sometimes  also,  when  in  the  vicinity  of  primitive  mountains, 
its  beds  are  thin,  and  much  bent  or  waved.  Beds  of  sand-stone  are 
sometimes  intersected  with  fissures  perpendicular  to  the  direction  of 
the  strata,  and  hence  fall  into  tabular  masses,  which  are  often  very 
large. 

Sand-stone  is  found  in  various  parts  of  the  United  States,  and  is, 
in  some  of  its  varieties,  very  useful  in  the  arts.  It  is  frequently 
known  by  the  name  of  free-stone.  When  sufficiently  solid,  it  is 
employed  as  a  building  stone.  In  most  cases,  it  is  of  moderate  hard- 
ness, and  cuts  equally  well  in  all  directions.  Some  varieties  natur- 
ally divide  into  prismatic  masses.  It  is  sometimes  used  as  mill- 
stones, for  grinding  meal,  or  for  wearing  down  other  minerals, 
preparatory  to  a  polish.  These  stones,  when,  rapidly  revolving, 
have  been  known  to  burst  with  a  loud  and  dangerous  explosion. 
When  the  texture  is  sufficiently  loose  and  porous,  it  is  employed  for 
filtering  water.    Some  varieties  are  used  for  whet-stones. 


OF  GNEISS. 


29 


Sand-stone  is  used  for  buildings,  in  various  parts  of  Europe.  In 
Africa,  the  temple  of  Hermopolis  is  composed  of  enormous  masses  of 
this  stone.  In  America,  the  Capitol  at  Washington  is  of  the  Poto- 
mac free,  or  sand-stone,  likewise  the  facade  of  St.  Paul's  Church,  in 
Boston. 


SECTION  IX.  Gneiss. 

This  rock,  like  granite,  is  composed  of  feldspar,  quartz,  and  mica. 
But  there  is,  in  gneiss,  less  feldspar  and  more  mica,  than  in  granite; 
but  even  in  this  substance  the  feldspar  appears  in  many  cases  to  be 
the  predominant  ingredient.  Its  structure  is  always  more  or  less 
distinctly  slaty,  when  viewed  in  the  mass  ;  although  individual 
layers,  composed  chiefly  of  feldspar  and  quartz,  may  possess  a  gran- 
ular structure.  The  layers,  whether  straight  or  curved,  are  fre- 
quently thick ;  but  often  vary  considerably  in  the  same  specimen  ; 
and  when  the  mineral  is  broken  perpendicular  to  the  direction  of 
the  strata,  its  fracture  has  commonly  a  striped  aspect.  It  splits 
easily  in  the  direction  of  the  strata,  especially  when  a  separation  is 
made  in  a  layer  of  mica.  When  gneiss  is  broken  in  the  direction  of 
the  strata,  the  mica  often  seems  more  abundant  than  the  other  ingre- 
dients, but  when  seen  on  the  cross  fracture,  it  obviously  exists  in 
less  proportion  than  the  feldspar  or  quartz. 

The  plates,  or  foliae  of  mica,  are  usually  arranged  parallel  to 
the  direction  of  the  strata,  and  in  some  varieties  are  chiefly  collected 
into  thin  parallel  layers,  separated  by  those  of  feldspar  and  quartz. 
The  grains  of  feldspar  are  often  flattened  in  the  direction  of  the 
strata. 

The  feldspar  is  usually  white,  or  gray,  sometimes  with  a  tinge  of 
yellow  or  red.  The  quartz  is  ordinarily  grayish  white  ;  and  the 
mica  is  often  black,  but  sometimes  gray. 

The  hardness  of  gneiss  is  variable  ;  and  the  feldspar  and  mica 
are  subject  to  the  same  changes  as  when  they  exist  in  granite. 

Gneiss,  like  granite,  never  embraces  any  petrifactions,  and  is 
always  a  primitive  rock. 

When  gneiss  occurs  with  granite,  it  usually  lies  immediately  over 
the  granite  ;  or,  if  the  strata  be  highly  inclined,  it  appears  rather  to 
rest  against  the  granite,  than  to  be  incumbent  upon  it. 

This  rock,  as  has  been  intimated,  assumes  sometimes  a  granular 
structure,  and  passes,  by  imperceptible  shades,  into  granite. 

Mountains,  composed  of  gneiss,  are  seldom  so  steep  as  those  of 
granite. — This  rock  is  abundant  in  the  United  States.  It  is  useful 
for  many  purposes,  in  consequence  of  the  facility  with  which  it 
splits  into  masses  of  regular  form. 


30 


OPERATIVE  MASONRY. 


SECTION  X.  Mica-Slate. 

Mica-Slate  is  essentially  composed  of  mica  and  quartz,  (see 
granite)  which  are  in  general,  more  or  less  intimately  mingled  ; 
but  sometimes  the  two  ingredients  alternate  in  distinct  layers.  Al- 
though the  proportions  of  mica-slate  are  variable,  the  mica  usually 
predominates. 

The  quartz  is  most  frequently  grayish  white  ;  but  the  mica  may 
be  whitish,  or  gray,  bluish  gray,  or  greenish,  brownish,  deep  blue, 
or  nearly  black. 

Its  structure  is  always  distinctly  slaty,  more  so  than  that  of  gne- 
iss ;  and  its  masses  are  often  very  fisile.  The  layers  are  sometimes 
straight,  and  sometimes  undulated.  In  some  varieties  the  texture 
is  very  fine,  and  the  foliae  of  mica  so  small,  that  they  are  scarcely 
discernible  by  the  eye,  unless  their  aggregation  be  previously  de- 
stroyed by  heat. 

This  rock  has  often  a  very  high  lustre,  when  viewed  by  the 
reflected  rays  of  the  sun.  It  is,  however,  subject  to  decomposition, 
by  which  its  aspect  is  much  altered. 

Mica-slate  is  a  primitive  rock  ;  but  seldom  appears  in  high,  steep 
cliffs,  like  those  of  granite.  When  it  forms  hills,  the  summits  are 
usually  much  rounded.  It  abounds  in  ores,  which  exist  both  in 
beds  and  veins  ;  but  more  frequently  in  beds.  It  is  less  abundant 
in  the  United  States  than  gneiss.  It  is  sometimes  split  into  tabular 
masses,  and  employed  for  many  common  purposes.  It  is  extremely 
useful  in  constructing  the  hearths  and  sides  of  furnaces  for  smelting 
iron. 


SECTION  XI.  Slate. 

Slate  is  an  argillaceous  stone,  characterized  by  easily  splitting 
into  large,  thin,  and  straight  layers^  or  plates,  which  are  sonorous 
when  struck  by  a  hard  body.  It  is  dull,  or  has  only  a  feeble  lustre. 
Its  colors  are  blackish  gray,  or  bluish  black,  bluish,  or  redish 
brown,  or  greenish,  &c. 

It  belongs  both  to  secondary  and  primary  rocks.  Its  structure 
en  masse,  is  tabular  ;  the  small  structure  lamellar  ;  the  cleavage  of 
the  laminae  being  parallel  with  the  tables. 

Slate  rocks  vary  in  hardness,  but  they  yield  to  the  knife.  They 
consist  of  an  intimate  intermixture,  in  various  proportions,  of  silice- 
ous earth,  alumine,  and  iron  ;  and  sometimes  contain  a  portion  of 
lime,  magnesia,  manganese,  and  bitumen.  Slate  forms  entire  moun- 
tains, and  sometimes  distinct  beds,  alternating  with  other  rocks.  It 
most  frequently  rests  on  granite,  gneiss,  and  mica-slate. 


OF  SLATE. 


31 


As  this  substance  forms  the  most  light,  elegant,  and  durable  cov- 
ering for  houses,  and  is,  of  course,  of  considerable  value  ;  it  is  ra- 
ther surprising  that  so  much  indifference  prevails  respecting  the 
search  for  it,  in  those  districts  where  common  slate,  or  clay  slate, 
abounds.  We  believe  all  the  roof  slate  quarries  at  present  worked, 
are  those  which  accident  has  discovered.  This  neglect  is  the  more 
remarkable,  when  we  consider  the  great  expense  frequently  incurred 
for  coal,  a  substance  of  less  value  in  proportion  to  the  weight. 

All  the  best  beds  of  roof  slate,  it  is  believed,  improve  as  they  sink 
deeper  into  the  earth  ;  and  few,  if  any,  are  of  a  good  quality  near 
the  surface,  or  are  indeed  suitable  for  the  purpose  of  roofing. 
There  cannot  be  a  doubt,  that  many  beds  of  slate,  which  appear 
shattered  and  unfit  for  architectural  use,  would  be  found  of  good 
quality  a  few  yards  under  the  surface  ;  for  the  best  slate,  in  many 
quarries,  loses  its  property  of  splitting  into  thin  laminae,  by  expo- 
sure to  the  air. 

Though  the  specific  gravity  of  slate  from  different  quarries  is  the 
same,  yet  all  the  sorts  are  not  capable  of  being  split  into  an  equal 
degree  of  thickness.  It  is  good  slate  which  will  split  into  laminae 
of  one  eighth  of  an  inch  in  thickness.  It  then  weighs  rather  more 
than  26  ounces  to  a  square  foot,  when  applied  to  the  covering  of  a 
roof.  In  some  instances,  slate  of  a  thinner  quality  is  used,  where 
cheapness  rather  than  durability  is  the  principal  object  of  the  archi- 
tect. According  to  an  estimate  of  Dr.  Watson,  the  relative  weights 
of  a  covering  of  the  following  different  materials,  for  forty-two 
square  yards  of  roof,  are 

Copper,  4  Cwt. 

Fine  Slate,  -  -  26  " 
Lead,          -       -     27  " 

Coarse  slate,  -  -  36  " 
Tile,    -       -  54  " 

Slate,  to  be  of  a  good  quality  for  building,  besides  possessing  the 
property  of  splitting  into  thin  laminae,  should  resist  the  absorption 
of  water;  to  prove  which,  it  should  be  kept  some  time  immersed 
in  water  ;  being  weighed  before  and  after  the  immersion,  wiping 
the  surface  dry  ;  it  is  obvious  that  the  slate,  which  gains  the  least 
weight  by  this  process,  is  the  least  absorbent.  It  should  resist  the 
process  of  natural  decomposition  by  air  and  moisture  ;  this  depends 
on  its  chemical  composition  and  compactness,  and  is  shown  by  its 
resisting  the  process  of  vegetation.  That  slate  which  is  most  liable 
to  decay,  will  be  the  soonest  covered  with  lichens,  mosses,  &c» 
The  hardness  of  slate  principally  arises  from  the  silex  it  contains, 
which  is  of  all  earths  the  least  favorable  to  vegetation.  Those  slates 
which  are  the  hardest,  when  first  taken  from  the  quarry,  and  which 
have  the  least  specific  gravity,  are  to  be  preferred  ;  for  the  increase 
in  weight  is  owing  to  the  presence  of  iron  ;  to  which  slate  and  other 
stones,  in  some  measure,  owe  their  decomposition  ;  while  alumine 
renders  them  soft  and  absorbent. 

Slate  is  so  durable,  in  some  cases,  as  to  have  been  known  to  con- 
tinue sound  and  good  for  centuries.  However,  unless  it  should  be 
brought  from  a  quarry  of  well  reputed  goodness,  it  is  necessary  to 


32 


OPERATIVE  MASONRY. 


try  its  properties,  which  may  be  clone  by  striking  the  slate  sharply 
against  a  large  stone,  and  if  it  produce  a  complete  sound,  it  is  a 
mark  of  goodness  ;  but  if  in  hewing,  it  does  not  shatter  before  the 
edge  of  the  instrument,  commonly  used  for  that  purpose,  the  crite- 
rion is  decisive.  The  goodness  of  slate  may  be  farther  estimated  by 
its  color  ;  the  deep  blue-black  kind,  is  apt  to  imbibe  moisture,  but 
the  lighter  blue  is  always  impenetrable.  The  touch,  also,  in  some 
degree,  may  be  a  good  guide,  for  a  good  firm  stone  feels  somewhat 
hard  and  rough,  whereas  an  open  slate  feels  very  smooth,  and  as  it 
were  greasy.  Another  method  of  trying  the  goodness  of  slate,  is  to 
place  the  slate-stone  lengthwise,  and  perpendicularly  in  a  tub  of 
water,  about  half  a  foot  deep,  care  being  taken  that  the  upper,  or 
unimmersed  part  of  the  slate,  be  not  accidentally  wetted  by  the  hand, 
or  otherwise  ;  let  it  remain  in  this  state  twenty  four  hours  ;  and  if 
good  and  firm  stone,  it  will  not  draw  water  more  than  half  an  inch 
above  the  surface  of  the  water,  and  that,  perhaps,  at  the  edges  only, 
those  parts  having  been  a  little  loosened  in  hewing  ;  but  a  spongy, 
defective  stone  will  draw  water  to  the  very  top. 

Roof  slate  is  found  in  Pennsylvania,  on  the  banks  of  the  Dela- 
ware, about  75  miles  from  Philadelphia,  of  a  good  quality.  In 
New- York,  at  New  Paltz,  Ulster  County  ;  and  at  Rhinebeck,  Duch- 
ess County.  In  Dummerston,  Vermont,  it  exists  in  strata  nearly 
vertical  ;  it  is  also  found  at  Rockingham,  and  Castleton,  where  it  is 
of  a  pale  red.  It  exists  in  Maine,  at  Waterville,  and  Winslow,  on 
the  Kennebeck  river. 

Extensive  quarries  of  slate,  of  a  good  quality,  are  worked  near 
Bangor,  England,  this  slate  is  exported  in  large  quantities  to  various 
parts  of  the  world. 

It  may  be  noticed,  that  in  laying  of  this  material,  a  bushel  and  a 
half  of  lime,  and  three  bushels  of  fresh  water  sand,  will  be  sufficient 
for  a  square  of  work  ;  but  if  it  be  pin  plastered,  it  will  take  about 
as  much  more  ;  but  good  slate  well  laid  and  plastered  to  the  pin, 
will  lie  an  hundred  years  ;  and  on  good  timber  a  much  longer  time. 
It  has  been  common  to  lay  the  slates  dry,  or  on  moss  only,  but  they 
are  much  better  when  laid  with  platter. 


SECTION  XII.  Soap-Stone,  or  Steatite. 

All  the  varieties  of  soap-stone  are  so  soft,  that  they  may  be  cut 
by  a  knife,  and  in  most  cases,  scratched  by  the  finger  nail.  Its 
powder  and  surface  are  soft,  and  more  or  less  unctuous  to  the  touch. 
It  is  seldom  translucent,  except  at  the  edges.  Its  fracture  is  in  gen- 
eral splintery,  earthy,  or  slaty,  with  little  or  no  lustre. 

By  exposure  to  the  heat,  it  becomes  harder,  but  is  almost  infusible 
by  the  blow  pipe.  It  appears  to  be  essentially  composed  of  silex, 
magnesia,  and  perhaps' alumine. 

The  common  variety  is  usually  solid  with  a  compact  texture  ;  its 
surface  is  often  like  soap  to  the  touch  ;  but  sometimes  it  is  found  of 
a  considerable  degree  of  hardness. 


OF  GYPSUM. 


33 


Its  color  is  usually  gray  or  white,  seldom  pure,  but  occasionally 
mixed  with  yellow,  green,  or  red,  and  is  sometimes  a  pale  yellow, 
redish,  or  green  of  different  shades.  The  colors  sometimes  appear 
in  spots,  veins,  &c. 

Its  specific  gravity  usually  lies  between  2.  58  and  2.  79 — when 
solid  it  is  somewhat  difficult  to  break.  Before  the  blow-pipe  it 
whitens  and  becomes  hard,  and  is  with  difficulty  reduced  into  a 
whitish  paste  or  enamel,  often  however  only  at  the  extremity  of  the 
fragment.  Some  specimens  have  yielded  by  analyzation,  silex,  64 
parts,  magnesia,  22.  alumine,  3.  water,  5.  iron  and  manganese,  5. 

Soap-stone  occurs  in  masses,  or  veins,  or  small  beds,  in  primitive 
and  transition  rocks,  more  particularly  in  serpentine.  It  is  some- 
times mixed  with  talc,  mica,  quartz  and  asbestus  ;  or  is  found  in- 
crusted  with  other  minerals. 

This  stone  is  not  uncommon.  It  is  found  in  various  parts  of  the 
United  States.  Among  the  best  quarries  for  fire-proof  stone,  is  that 
of  Francestown,  New-Hampshire.  It  occurs  also,  in  Connecticut, 
near  New  Haven,  and  at  Oxford,  Grafton,  and  Athens,  in  Vermont. 

Soap-stone,  on  account  of  its  softness,  is  wrought  with  the  same 
tools  as  wood.  It  receives  a  tolerable  polish,  and  is  sometimes  used 
in  building,  but  is  not  always  durable.  It  is,  however,  of  great  im- 
portance in  the  construction  of  fire  places  and  stoves,  and  is  exten- 
sively used  for  this  purpose.  Slabs  of  good  soap-stone,  when  not 
exposed  to  mechanical  injury,  frequently  last  eight  or  ten  years, 
under  the  influence  of  a  common  fire  on  one  side,  and  of  cold  air 
on  the  other.  It  grows  harder  in  the  fire,  but  does  not  readily 
crack,  nor  change  its  dimensions  sufficiently  to  affect  its  usefulness. 
Owing  to  the  facility  with  which  it  is  wrought,  its  joints  may  be 
made  sufficiently  tight  without  dependence  on  cement. 

It  is  often  wrought  into  various  utensils  by  turning,  and  is  advan- 
tageously employed  for  aqueducts.  It  has  been  found  to  be  one  of 
the  best  materials  for  counteracting  friction  in  machinery,  for  which 
purpose  it  is  used  in  powder,  mixed  with  oil.  It  has  also  been 
employed  for  the  purpose  of  engraving.  By  being  easily  cut,  when 
soft,  it  may  be  made  to  assume  any  desired  form,  and  afterwards 
rendered  hard  by  heat ;  it  then  becomes  susceptible  of  a  polish,  and 
may  be  variously  colored  by  metallic  solutions. 


SECTION  XIII.  Gypsum. 

Gypsum  is  a  term  applied  in  its  restricted  sense  to  those  varieties 
of  sulphate  of  lime,  which  have  a  fibrous  or  granular  structure,  being 
the  result  of  confused  crystallization,  and  to  those,  whose  texture  is 
compact,  or  earthy.  It  is  a  substance  that  is  interesting  on  account 
of  its  uses  in  agriculture  and  the  arts.  Its  colors  are  commonly 
white  or  gray,  sometimes  shaded  with  yellow,  red,  or  variously 
mingled. 

It  occurs  in  compact  masses,  sometimes  granular,  and  sometimes 
in  parallel  fibres.    Though  sometimes  coarse,  the  fibres  are  often 


34 


OPERATIVE  MASONRY. 


fine  and  delicate,  glistening  with  a  pearly  satin  lustre.  Its  fracture 
is  foliated,  sometimes  splintery  ;  it  is  generally  translucent,  often  in 
amorphous  masses  ;  but  not  unfrequently  crystallized.  It  is  less 
hard  than  carbonate  of  lime.  Its  specific  gravity  usually  lies  be- 
tween 2.  26  and  2.  31.  By  the  blow-pipe  it  may  be  melted,  though 
not  very  easily,  into  a  white  enamel,  which  shortly  falls  into  a  pow- 
der. It  does  not  effervesce  with  acids,  if  it  be  pure  sulphate  of  lime. 
It  is  soluble  in  about  500  times  its  weight  of  water.  It  does  not 
burn  to  lime. 

It  is  composed  of  32  parts  of  lime,  46  of  sulphuric  acid,  and  22 
parts  of  water  ;  but  it  is  often  contaminated  with  small  quantities  of 
carbonate  of  lime,  alumine,  silex,  and  oxide  of  iron.  Some  varie- 
ties are  employed  in  sculpture  and  architecture  under  the  name  of 
alabaster  ;  the  same  name  is  also  given  to  some  varieties  of  carbonate 
of  lime. 

The  Plaster  Stone,  or  Plaster  of  Paris,  often  contains  foreign  in- 
gredients,  which,  in  many  instances,  improve  it  as  a  cement. 

This  substance  is  found  in  abundance  in  many  places,  and  has 
been  extensively  used  for  manure  in  dressing  land,  and  appears  to 
be  useful  in  both  clayey  and  sandy  soils.  It  is  also  employed  in 
the  imitative  and  ornamental  arts.  Alabaster,  both  of  the  sulphate 
and  carbonate  kinds,  has  been  used  for  the  same  purposes  as  marble 
in  architecture  and  statuary  ;  and  being  less  hard  it  is  more  easily 
wrought ;  but  is  less  durable  and  less  valuable  than  marble.  Gyp- 
sum, when  deprived  of  its  water  of  crystallization  by  burning  or 
drying,  constitutes  Plaster  ;  and  this  plaster,  when  mixed  with  a  cer- 
tain quantity  of  quick-lime,  forms  a  good  cement.  The  Plaster  of 
Paris  often  contains,  in  its  natural  state,  a  sufficient  quantity  of  car- 
bonate of  lime  to  constitute  a  good  cement  after  calcination. 

The  finer  kinds  of  Plaster,  being  reduced  to  powder,  and  mixed 
with  water,  have  the  property  of  becoming  hard  in  a  few  minutes, 
and  of  receiving  accurately  the  impressions  of  the  most  delicate  mod- 
els. It  is  extensively  employed  in  stucco  work,  and  in  plastering 
rooms.  It  furnishes  a  delicate,  white  and  smooth  material  for  ar- 
chitectural models,  impressions  of  seals,  &c;  and  in  the  art  of  stere- 
otyping it  is  indispensable.  In  stucco,  various  colors,  previously 
ground  in  water,  may  be  introduced.  All  these  works,  when  dry, 
are  susceptible  of  a  polish. 

The  Temple  of  Fortune,  called  Seja,  appears  to  have  been  built 
with  some  variety  of  sulphate  of  lime.  It  had  no  windows,  but 
transmitted  a  mild  light  through  its  walls. 


SECTION  XIV.  Puzzolana. 

This  substance  is  of  volcanic  origin.  It  usually  occurs  in  small 
fragments,  or  friable  masses,  which  have  a  dull,  earthly  aspect  and 
fracture,  and  seems  to  have  been  baked.  Its  solidity  does  not  ex- 
ceed that  of  chalfc.    It  is  seldom  tumefied,  and  its  pores  are  neither 


i 


OF  TRAS,  OR  TERAS. 


35 


large  or  numerous.     Its  colors  are  gray  or  whitish,  reddish  or 
nearly  black. 

By  exposure  to  the  heat  it  melts  into  a  black  slag.  A  variety  ex- 
amined by  Bergaman,' yielded  55  to  GO  parts  of  silex,  19  to  20  of  al- 
umine,  15  to  20  of  iron,  and  5  to  6  parts  of  lime.  It  often  contains 
distinct  particles  of  pumice,  quartz  and  scoria. 

This  substance  is  extremely  useful  in  the  preparation  of  a  mortar,  . 
which  hardens  quickly,  even  under  water.  When  thus  employed  it 
is  mixed  with  a  smali  proportion  of  lime,  perhaps  one  third.  It  has 
been  supposed  that  the  rapid  induration  of  this  mortar  arises  from 
the  very  low  oxidation  of  the  iron.  If.  the  mortar  be  a  long  time 
exposed  to  the  air,  previous  to  its  use,  it  will  not  harden.  The  best 
puzzolana  is  said  to  occur  in  old  currents  of  lava  ;  but  when  too 
earthy  it  loses  its  peculiar  properties.  That  which  comes  from 
Naples  is  generally  gray. 


SECTION  XV.  Tras,  or  Terras. 

*  The  nature  of  this  is  similar  to  some  varieties  of  puzzolana  ;  and 
it  contains  nearly  the  same  principles,  but  with  a  greater  proportion 
of  lime.  Its  hardness  is,  however,  much  greater,  than  that  of  puz- 
zolana. Its  color  is  brownish  or  yellowish  ;  and  its  fracture  earthy 
and  dull.  It  has  been  found  chiefly  near  Andernach,  in  the  vicinity 
of  the  Rhine. 

It  is  said  to  be  decomposed  basalt.  It  forms  a  durable  water  ce- 
ment when  combined  with  lime.  It  is  the  material  which  has  been 
principally  employed  by  the  Dutch,  whose  aquatic  structures  prob- 
ably exceed  those  of  any  other  nation  in  Europe.  Terras  mortar, 
though  very  durable  in  water,  is  inferior  to  the  more  common  kinds, 
when  exposed  to  the  open  air. 


SECTION  XVI.  Quarrying. 

The  common  methods  of  working  and  managing  different  sorts 
of  quarries,  are  in  general  pretty  well  understood,  by  such  quarry- 
men  as  are  constantly  employed  in  the  business.  The  materials  are 
indicated  by  the  appearance  of  the  surface  of  the  earth,  the  nature 
of  the  substances  in  the  vicinity,  or  by  digging  down  and  opening 
the  ground  by  spades  and  other  tools,  or  by  boring  with  an  auger 
made  for  the  purpose. 

The  great  value  to  mankind  of  such  materials  as  coal,  iron  ores, 
&c.  as  well  as  of  building  materials,  should  induce  proprietors  of 
land  to  cause  a  more  diligent  and  scientific  search  for  these  hidden 
treasures,  than  has  been  hitherto  practised  in  this  country.  It  may 
also  be  suggested,  that  it  would  be  highly  beneficial  and  advanta- 
geous, if  mineralogists,  and  those  who  have  an  acquaintance  with 


36  OPERATIVE  MASONRY. 

such  substances,  were  to  turn  their  attention  towards  the  appear- 
ances and  accompaniments,  which  point  out  such  useful  concealed 
matters  ;  as  it  might  greatly  facilitate  the  search  for  them,  and  fre- 
quently lead  fortuitously  to  their  discovery.  In  searching  for  most 
sorts  of  mineral  substances,  coals,  and  some  other  matters,  the  use  of 
the  borer  is  almost  constantly  resorted  to  ;  but  with  regard  to  lime- 
stone, free-stone,  granite,  &c,  digging  down  into  the  earth  is  the 
mode  commonly  employed  in  the  first  instance,  in  consequence  of 
such  substances  being  obviously  present  in  sufficient  quantities  to  be 
wrought  with  advantage. 

When  it  has  been  ascertained  that  the  material  exists  in  sufficient 
quantity  to  warrant  the  working  of  the  quarry,  much  time  and  ex- 
pense will  be  saved,  by  proceeding  in  a  correct  manner  in  the  first 
opening  of  it. 

Instead  of  beginning  to  dig  at  the  top,  by  which  means  the  pro- 
gress of  the  workmen  will  soon  be  impeded  by  accumulating  rub- 
bish, or  the  rushing  in  of  water,  it  would  be  far  preferable  to  com- 
mence on  one  side  of  the  elevation  which  contains  the  material, 
having  previously  ascertained  which  way  the  rocks  incline  or  dip, 
and  gradually  approach  the  quarry,  on  this  side  ;  clearing  away  the 
dirt  and  superincumbent  substances  as  low  down  as  the  nature  of 
the  ground  will  admit.  In  this  manner,  the  mouths  or  openings  of 
the  quarries  may  be  easily  kept  free,  and  the  water  carried  off ;  at 
the  same  time,  the  materials  may  be  operated  upon,  and  removed 
with  the  greatest  facility.  If  the  nature  of  the  situation  admits  of 
the  opening  of  a  quarry  in  this  manner,  the  more  convenient  method 
of  working  it  is,  by  gradations  or  steps.  That  is,  the  stone  is  first 
taken  from  the  top  to  an  uniform  depth  for  a  considerable  distance 
back  ;  then  another  stratum  or  layer  is  removed  till  it  approaches 
within  some  distance  of  the  first,  when  a  third  is  began,  and  so  on  ; 
so  that  the  quarry  presents  the  appearance  of  steps,  or  horizontal 
planes  one  above  the  other.  This  method  affords  facilities  for  re- 
moving the  stone,  or  materials  without  the  aid  of  expensive  machi- 
nery . 

There  is  often  a  great  difference  in  the  quality  of  the  material  in 
the  same  quarry.  Those  portions,  which  are  nearest  to  the  surface, 
are  sometimes  mixed  with  foreign  ingredients,  that  impair  their 
value,  or  render  them  useless. 

The  stones  are  obtained  of  suitable  dimensions  by  blasting,  by 
splitting  with  iron  wedges  set  in  a  direct  line,  and  driven  with 
much  force  by  a  sledge  or  hammer.  Advantage  is  often  taken  of 
natural  fissures  which  are  in  straight  lines,  and  often  at  right  angles. 

Granite,  and  the  stones  related  to  it,  although  of  great  hardness, 
will  split  very  straight  by  means  of  wedges.  The  pieces  are  after- 
wards wrought  into  the  form  to  be  used,  either  at  the  quarry, 
which  diminishes  the  expense  of  transportation,  or  removed  in  a 
rough  state,  and  thus  used  in  building  ;  or  finished,  as  may  be 
deemed  expedient. 

In  working  granite,  and  materials  of  a  similar  nature,  it  is  first 
lined,  or  marked  into  the  form  desired.  The  workman  then  forms 
the  edge  all  round  by  means  of  a  chissel  and  hammer,  making  it 
smooth  and  straight  to  the  depth  of  one  or  two  inches  ;  he  after- 


OF  QUARRYING. 


37 


wards  breaks  off  the  larger  portions  with  a  hammer  made  in  a  pecu- 
liar form,  and  kept  sharp  ;  with  this  instrument  he  continues  to 
take  off  the  inequalities  of  the  surface,  till  it  has  the  requisite 
smoothness. 

Sand-stone,  free-stone,  and  materials  of  the  like  nature,  being  less 
hard  than  granite,  are  more  easily  wrought  by  a  similar  process. 
Some  of  them  admit  of  a  considerable  degree  of  polish. 

Marble  and  soap-stone  are  taken  from  the  quarries  in  large  masses, 
and  afterwards  sawed,  either  by  hand,  or  in  mills  constructed  for 
the  purpose,  and  then  polished,  (see  Marble  and  Soap- Stone.)  Slate, 
in  some  instances,  is  obtained  by  blasting.  It  is  sometimes  dug  out 
by  one  set  of  men,  split  by  another,  and  formed  into  slates  by  a 
third  ;  for  which  purposes,  flat  crow-bars,  slate-knives,  and  axes 
are  employed.  It  is  often  divided  into  three  sorts,  as  firsts,  seconds, 
and  thirds,  which  vary  in  quality  and  price. 

Sand  and  gravel  are  mostly  dug  out  from  the  sides  of  banks,  and 
other  places  ;  and  but  rarely  obtained  by  sinking  the  quarries  into 
the  more  level  parts  of  the  ground,  though  this  method  is  sometimes 
practised.  The  materials  are  commonly  raised,  simply  by  digging 
with  spades  ;  and  thrown  into  carts,  in  many  cases,  from  the  quar- 
ries, or  pits  themselves. 

The  removal  of  materials  from  quarries,  is  effected  by  means  of 
inclined  planes,  of  rail-ways,  or  by  various  machines  constructed  for 
the  purpose,  such  as  the  windlass,  the  pulley,  &c.  adapted  in  each 
instance  to  the  situation  of  the  quarry,  and  the  circumstances  of  the 
case. 

The  Quincy  stones  are  raised  from  their  beds  by  the  means  of 
a  windlass  worked  by  a  horse,  and  received  upon  cars,  which  run 
upon  inclined  rail-ways,  within  a  few  feet  of  the  quarry  ;  from 
thence  they  are  conveyed  to  the  sea  on  a  rail-way,  and  transported 
in  various  directions.  By  the  descent  of  a  loaded  car  on  the  inclined 
rail-way  at  the  quarry,  an  empty  car  is  drawn  up. 

The  greatest  difficulty  incident  to  working  quarries,  is  that  of 
draining ,  and  freeing  their  bottom  parts  from  injurious  water  ;  so 
that  they  may  be  in  a  fit  state  to  be  wrought  with  ease  and  advan- 
tage. 

The  most  usual  remedies,  resorted  to  in  this  difficulty,  are  pumps, 
worked  by  wind,  by  horse,  steam,  or  other  powers  ;  but  these  often 
prove  ineffectual  in  removing  the  water  completely,  and  new  quar^ 
ries  are  opened  near  the  old  ones.  But  an  attention  to  certain  prin- 
ciples, in  regard  to  the  nature  of  the  soil,  and  the  courses  of  subter- 
raneous waters,  may  often  lead  to  more  cheap,  expeditious,  and 
effectual  remedies. 

It  is  now  well  understood,  that  most  springs,  and  subterraneous 
collections  of  water  are  formed  and  supplied  from  such  grounds 
as  lie  higher  than  that  of  the  places  where  the  waters  are  met 
with,  which,  in  consequence  of  their  being  of  an  open  and  porous 
nature,  admit  the  rain  and  other  sorts  of  moisture  to  filtrate  and 
pass  freely  through  them.  These  waters  descend  to  great  depths 
before  they  become  impeded  by  some  sort  of  impenetrable  stratum, 
or  layer  of  a  solid  or  stony  nature,  as  clay,  or  compact  rock.  It 
may  happen,  in  sinking  quarries,  that  beds  of  quicksand  may  be 


38 


OPERATIVE  MASONRY. 


met  with,  which  are  so  full  of  water,  that  to  penetrate  through  them 
will  be  very  difficult  ;  and  from  a  knowledge  that  the  water  pro- 
ceeds from  the  porous  ground  that  lies  above  them,  it  may  be  prac- 
ticable to  intercept  and  cut  off  the  greater  part  of  it  before  it 
reaches  the  sand  beds  in  the  quarries,  by  the  means  of  boring  into 
and  tapping  the  water  at  the  tails  of  the  banks  of  this  nature,  pro- 
vided,  that  the  ground  declines  lower  than  the  place  where  the  sand 
is  found  in  the  quarries,  which  may  be  done  at  a  trifling  expense, 
in  comparison  to  the  common  remedies. 

But  in  order  to  accomplish  this  intention,  it  will  be  necessary,  in 
ascending  from  the  quarry,  to  ascertain  if  at  the  place  higher,  on  the 
declivity,  any  porous  stratum,  bed  of  rock,  sand  or  gravel,  tails  out, 
which  may  convey  the  water  contained  in  it  to  the  sand  bed,  which 
is  below  in  the  works  ;  and  where  any  such  is  found,  to  cut  and  bore 
into  it,  in  such  a  manner  as  to  form  a  drain,  that  is  capable  of  con- 
veying off"  the  water,  which  would  otherwise  have  descended  into 
the  quarry. 

But  although  this  part  of  the  business  may  have  been  accom- 
plished, and  the  supply  of  water  from  the  higher  ground  entirely 
cut  off,  a  sufficient  quantity  to  injure  and  inconvenience  the  work- 
ing may  yet  continue  to  drain  from  the  sides  of  the  sand  beds, 
though  they  should  happen  to  dip  towards  the  lower  ground  ;  in 
which  cases,  however,  this  water  may  be  drawn  off  readily  to  some 
particular  point. 

In  order  to  effect  this,  it  should  be  ascertained,  at  what  particular 
place  in  the  low  ground  the  sand  terminates,  or  tails  out,  which  is 
the  best  accomplished  by  means  of  proper  levelling  ;  and  if  there 
should  be  any  appearance,  in  this  place,  of  the  water's  having  a  nat- 
ural outlet,  it  may,  by  making  it  into  a  deep  drain,  cause  the  water 
effectually  to  be  drawn  off.  Where,  however,  there  happens  to  be 
a  deep,  impervious  layer  of  clay,  or  other  matter  of  a  similar  nature, 
placed  above,  or  upon  the  termination,  or  tail  of  the  sand,  the  drain 
need  only  be  cut  down  to  it,  or  a  little  way  into  it,  as  by  means  of 
boring  through  it,  a  ready  and  easy  passage  may  be  given  to  the 
whole  of  the  water,  contained  in  the  sand  bed,  or  porous  stratum. 

It  is  of  material  importance  to  lay  dry  all  such  grounds  as  are 
situated  higher,  but  contiguous  to  quarries,  for  the  above  stated 
reasons,  and  it  may  in  general  be  accomplished  with  but  little  diffi- 
culty and  expense,  by  adopting  the  same  principles,  and  the  same 
means. 

This  is  the  mode  that  is  to  be  pursued  in  preventing  the  effects 
of  the  water,  or  cutting  it  off,  when  met  with  in  sinking  quarries.  It 
proceeds  on  the  principle  of  the  dipping  position  of  the  strata 
with  the  natural  inclination  of  the  land. 

It  frequently  happens,  that  a  body  of  the  same  stone,  which  is  of 
a  close  and  compact  nature,  is  found  lying  under  one,  which  has  a 
more  open  and  porous  texture,  with  fissures  and  cracks  in  it,  that 
are  admissible  of  water,  in  the  upper  body  or  layer,  in  such  a 
manner  that  none  can  pass  through  it  to  the  inferior,  or  still  deeper, 
open  stratum,  or  bed  ;  and  on  sinking,  or  cutting  through  this 
compact  bed,  another  layer  is  met  with,  which  is  of  so  porous 
a  nature  as  to  admit  the  reception  of  any  water,  that  may  come 


OF  QUARRYING. 


89 


upon  it.  And  sometimes  a  bed  of  gravel,  or  sand  is  found  under 
that  of  close  stone,  which  being  capable  of  absorbing  any  water  that 
may  come  upon  it,  and  which  is  far  better  suited  for  the  purpose  of 
clearing  the  upper  bed  of  stone  from  water,  than  the  stratum  of  open 
stone  itself.  Therefore,  when  this  is  ascertained  to  be  the  case,  and 
the  water  is  kept  up  by  the  second  bed  of  stone,  so  as  to  be  injuri- 
ous to  the  working  of  the  upper  bed,  and  which  will  be  equally  so 
in  working  the  second  ;  the  work  may  be  greatly  freed  by  boring 
through  the  close  bed  of  stone,  and  letting  the  water  down  into  the 
more  porous  one  below,  or  into  a  stratum  of  dry  sand,  or  gravel, 
should  there  be  such  a  one  underneath  it.  But  instead  of  boring, 
the  sinking  of  small  pits  through  the  close  stone,  is  a  more  effectual 
way  of  letting  down  the  water. 

In  all  such  cases  as  these,  boring  or  sinking  pits  through  the  solid 
stratum  into  a  porous  substance,  or  layer,  underneath,  is  the  most 
advisable,  and,  at  the  same  time,  the  least  expensive  method,  that 
can  be  pursued. 


G 


TABLE. 


The  following  table  shows  the  weight  of  granite  stone  in  lbs.  and  lOOths,  both  in 
a  cubical  and  cylindrical  form  ;  the  dimensions  being  given.  The  first  column  of 
figures  denotes  a  piece  of  stone  to  be  1,  2,  3,  &c.  inches  square,  or  in  diameter ; 
each  piece  being  12  inches  in  length.  Columns  2  and  3  are  the  mean  weight  of 
common  stone ;  4  and  5  the  weight  of  the  Quincy  stone ;  6  and  7,  the  weight  of 
a  species  of  coarse  granite,  found  at  Sandy  Bay,  in  Massachusetts. 


MEAN  WEIGHT  OF 
STONE    IN  GENERAL. 


QUINCY  GRANITE. 


SANDY  BAY  GRANITE. 


Square.     Cylindric.  \\ 

o  QUCLTt. 

(^ylindftc.  [I 

iJl£tttll  t» 

bo 
P 

1 

1,07 

,86 

1,16 

,95 

1,17 

,95 

2 

4,33 

3,45 

4,65 

3,80 

4,68 

3,80 

o 

3 

9,70 

7,75 

10,44 

8,55 

10,53 

8,56 

<M 

o 

4 

17,33 

13,80 

18,56 

15,20 

18,72 

15,21 

one  f< 

5 

97  DO 

29,00 

23,75 

29,22 

23,77 

6 

38,10 

31,00 

41,76 

34,20 

42,12 

34,23 

7 

52,67 

42,00 

55  88 

57  33 

44  59 

-a 

8 

69,00 

55,00 

74^24 

60,80 

74^88 

60,86 

d 

9 

86,67 

69,65 

83,96 

76,95 

94,77 

77,03 

a 

10 

107,33 

86,00 

116,00 

95,00 

117,00 

95,10 

11 

130,00 

104,00 

140,36 

114,95 

141,57 

115,07 

12 

155,00 

124,00 

167,04 

136,80 

168,48 

136,94 

to 
a 

1 

5,35 

4,30 

I  5,80 

4,75 

5,85 

[  4,75 

2 

23,65 

17,25 

23,20 

19,00 

•  23,40 

19,40 

o 

3 

48,50 

38,75 

52,20 

42,75 

52,65 

42,80 

a 

4 

86,65 

69,00 

92,80 

76,00 

93,60 

75,05 

5 

135,00 

107,50 

145,00 

118,75 

146,10 

118,85 

> 

6 

190,50 

155,00 

200,80 

171,00 

210,00 

171,15 

n 

7 

263,35 

310,00 

379,20 

232,75 

286,65 

222,95 

8 

345,00 

275,00 

37 1 ,20 

304,00 

374,40 

304,30 

a 

9 

433,35 

348,00 

419,80 

384,75 

473,85 

385,15 

J 

10 

5S6y65 

430,00 

580,00 

475,00 

585,00 

475,50 

H 

11 

650,00 

520,00 

701,80 

574,75 

707,85 

575,35 

12 

775,00 

620,00 

835,20 

680,00 

842,40 

684,70 

1 

10,70 

8,60 

11,60 

9,50 

11,70 

9,50 

b*D 

a 

2 

43,30 

34.50 

46,40 

38,00 

56.80 

38,00 

3 

97,70 

77,50 

104,40 

85,50 

105,30 

85,60 

•*-» 
<D 

4 

173,30 

138,00 

185,60 

152,00 

187,20 

152,10 

tg 

5 

270,00 

215,00 

290,00 

•237,50 

292,20 

237,70 

C 

» 

6 

381,00 

310,00 

417,60 

342,00 

421,20 

342,30 

a 

7 

526,70 

420,00 

558,40 

465,50 

573,30 

445,90 

8 

690,00 

550,00 

742,40 

608,00 

748,80 

608,60 

a> 

CS 

9 

866,70 

696,00 

839,60 

769,50 

947,70 

770,30 

a 

10 

1073,00 

860,00 

1160,00 

950,00 

1170,00 

951,00 

H 

11 

1300,00 

1040,00 

1403,00 

1149,00 

1415,70 

1150,70 

12 

1550,50 

1240,00 

1670,40 

1368,00 

1684,80 

1369,40 

RULES 

FOR  MEASURING  HAMMERED  GRANITE  STONE, 

ADOPTED  APRIL,  1829. 


PREAMBLE. 

To  prevent  misunderstanding  between  the  Stone  Cutters,  the  Masons 
and  their  employers,  in  relation  to  the  admeasurement  of  hammered  Granite 
Stone,  it  was  deemed  expedient,  that  a  meeting  be  called  of  those  engaged  in 
the  business,  to  endeavor  to  agree  upon  some  uniform  system,  that  shall  be 
equally  intelligible  to  all  parties ;  said  meeting  was  held  in  March  last,  when  a 
Committee  of  eleven  persons  were  chosen,  to  take  the  subject  into  consideration, 
and  report  at  a  subsequent  meeting.  At  a  meeting  in  April,  said  committee 
reported,  that  they  had  attended  to  the  duty  assigned  them,  and  after  mature 
deliberation,  have  agreed  on  the  following  Rules,  which,  if  adopted,  will,  in 
their  opinion,  greatly  promote  the  interest,  as  well  as  the  harmony  of  all  con- 
cerned in  the  business,  whether  purchaser  or  vender;  at  which  meeting  said 
Rules  were  adopted  by  the  unanimous  vote  of  all  present,  who  then  affixed  their 
signatures  to  the  same,  since  which,  others  have  subscribed  their  names. 

Boston,  May  17,  1829. 

RULES,  &c. 

Section  1.  ASHLER  STONES  are  to  be  measured  on  their  fronts, 
quoin  heads,  and  reveals  against  doors,  windows  and  recesses. 

Sec.  2.  HEADERS,  or  binders  that  make  the  thickness  of  the  wall, 
are  to  be  measured  as  Ashler  work,  adding  their  beds,  or  builds. 

Sec.  3.  DOUBLE  HEADED  QUOINS,  not  less  than  9  inches  each 
head,  are  to  be  measured  as  Ashler  work,  adding  their  beds,  or  builds. 

Sec.  4.  WINDOW  CAPS  for  Ashler  work,  are  to  be  measured  on 
their  fronts,  under  sides  that  show,  and  reveals. 

Sec.  5.  WINDOW  SILLS  for  Ashler  work,  are  to  be  measured  on 
their  tops  and  fronts,  the  whole  thickness  of  their  rise,  and  half  their  under 
sides, 


42 


OPERATIVE  MASONRY. 


Sec.  6.  BELT  STONES  for  Ashler,  or  Brick  work  from  7  to  9  inches 
rise,  and  the  usual  thickness  of  Ashler  work,  are  to  be  cast  at  the  rate  of 
a  superficial  foot  to  each  foot  in  length. 

Sec.  7.  ARCH  STONES  in  Ashler  work,  are  to  be  measured  their 
extreme  lengths  by  their  extreme  widths,  adding  the  returns  and  reveals. 

Sec.  8.  ASHLER  STONES  for  Pediments  or  Gable-ends  of  buildings, 
and  other  similar  purposes,  are  to  be  measured  their  extreme  lengths,  by 
their  extreme  widths. 

Sec  9.  PLINTHS  are  to  be  measured  on  all  parts  that  show,  and 
half  the  rough  hammered  parts. 

Sec  10.  PILASTERS  are  to  be  measured  on  their  fronts,  returns  and 
reveals. 

Sec  11.  IMPOSTS  are  to  be  measured  on  their  fronts,  ends  and  beds, 
or  builds. 

Sec  12.  POSTS  or  CAPS,  are  to  be  measured  on  four  sides,  and  the 
ends  of  caps  that  show. 

Sec  13.  POSTS  in  or  out  of  square,  are  to  be  measured  on  four  sides, 
squaring  from  their  extreme  points. 

Sec  14.  DOOR  SILLS,  under  Posts,  are  to  be  measured  on  their  tops, 
fronts  and  ends,  and  half  the  parts  hammered  under  the  ends. 

Sec  15.  WINDOW  SILLS  between  Posts,  are  to  be  measured  on 
their  tops,  under-sides,  and  their  whole  rise. 

Sec  16.  ARCH  CAPS  and  BLOCKS,  that  make  the  thickness  of 
the  wall,  are  to  be  measured  on  four  sides,  the  extreme  lengths  by  their  ex- 
treme widths. 

Sec  17.  BELT  STONES  that  make  the  thickness  of  the  wall,  are  to 
be  measured  on  their  fronts,  beds  and  builds,  and  ends  that  show. 

Sec  18.  COURSES  of  STONES  that  make  the  thickness  of  the  wall, 
are  to  be  measured  on  their  fronts,  beds  and  builds. 

Sec  19.  DOOR  STEPS,  are  to  be  measured  on  their  tops,  fronts  and 
laps,  and  the  ends  that  show,  which  ends  are  to  be  measured  at  the  rate  of 
a  superficial  foot  to  each  foot  on  the  width. 

Sec  20.  RETURNS  for  Steps,  from  6  to  10  inches  rise,  are  to  be 
measured  at  tihe  rate  of  a  superficial  foot  to  each  foot  in  length. 


RULES  FOR  MEASURING  HAMMERED  GRANITE.  43 


Sec.  21.  PLATFORM  STONES  are  to  be  measured  as  Steps,  when 
two  or  more  are  required,  half  the  edges  for  joints  are  to  be  added. 

Sec.  22.  SPIRAL  STEPS  are  to  be  measured  their  extreme  length 
by  their  extreme  width,  rise  and  laps,  and  ends  that  show. 

Sec.  23.  FENCE  STONES  are  to  be  measured  on  their  fronts,  tops 
and  inside,  where  hammered,  and  ends  that  show. 

_Sec.  24.  POSTS  that  stand  in  the  ground,  are  to  be  measured  on 
four  sides  and  tops,  and  half  measurement  of  the  rough  parts  in  the  ground, 
according  to  the  dimensions  of  the  hammered  parts. 

Sec.  25.  CELLAR  DOOR  CURBS  are  to  be  measured  on  their 
tops  and  inside,  or  rise,  the  whole  length  of  each  stone,  the  rabbets  are  to 
be  measured  the  length  of  each  stone  by  the  running  foot. 

Sec  26.    CELLAR  WINDOW  CURBS  are  furnished  by  the  piece. 

Sec.  27.  WELL  CURBS  are  to  be  measured  on  the  outside  and  tops, 
where  hammered  with  the  jogs  and  corresponding  ends. 

Sec.  28.  SESS  POOL  CURBS  are  to  be  measured  as  Cellar  Door 
Curbs. 

Sec.  29.  GUTTER  STONES  are  to  be  measured  on  the  top  side  by 
the  superficial  foot ;  Cutting  Gutters  to  be  charged  extra. 

Sec.  30.  EDGE  STONES  are  to  be  measured  by  the  running  foot, 
double  measure  when  circular. 

Sec.  31.  CUTTING  SCROLES,  JOGS,  RABBETS,  GROVES, 
GUTTERS,  and  DRILLING  HOLES,  are  extra  work,  and  do  not  add 
to,  or  diminish  from  the  measurement  of  the  work. 

Sec.  32.  VAULT  STONES  are  to  be  measured  on^  three  or  four 
sides,  as  may  be  hammered,  and  the  ends  that  show.  Floor  and  Ceiling 
Stones  more  than  9  inches  in  thickness,  are  to  be  measured  on  one  side  and 
two  edges,  and  the  ends  that  show ;  when  9  inches  or  less  thickness,  on 
one  side  and  ends  that  show. 

Sec.  33.  All  STONES  not  included  in  the  foregoing  specifications,  on 
account  of  their  irregular  form  or  unfrequent  use,  should  be  measured  as 
nearly  as  possible  according  to  the  rules  applying  to  those  which  resemble 
them. 

Sec.  34.  Those  which  differ  in  all  respects,  must  be  furnished  by  the 
piece. 


44 


OPERATIVE  MASONRY. 


Sec.  35.  The  two  foregoing  observations  apply  to  Ornamental  Work, 
the  parts  of  which  are  so  minute,  and  generally  of  such  complicated  forms, 
that  no  system  of  rules  sufficiently  short  and  comprehensive,  can  with  any 
utility  be  adopted  ;  with  regard  however  to  two  or  three  parts  of  Ornamen- 
tal Work,  in  common  use,  it  may  be  well  to  state,  that  Cornice  is  usually 
furnished  by  the  running  foot;  Bases,  Columns  and  Capitals,  by  the  piece. 

Sec.  36.  All  Circular  Work  to  be  charged  extra,  and  the  mode  of 
measurement  should  be  agreed  upon  at  the  time  said  work  is  contracted  for. 


William  Austin. 

Gridley  Bryant, 
Benjamin  Blaney, 
Jacob  Bacon. 

William  Crehore, 
Samuel  Currier, 
Levi  Cook, 
Conrad  C.  Carleton. 

James  C.  Eiver,  Jr., 
George  H.  Ewer. 

Joseph  Glass. 

Ephraim  Harrington, 
Thomas  Hollis, 
Charles  G.  Hall. 

Samuel  R.  Johnson, 
Nathaniel  Jeivett. 

Sewall  Kendall. 

Allen  Litchfield,  Jr., 
Ward  Litchfield, 
Francis  Lawrence. 

James  McAllaster, 
Caleb  Metcalf, 
Samuel  Marden, 


Luther  Munn. 

Jonathan  Newcomb, 
Cushing  Nichols. 

Alexander  P  arris, 
James  Page, 
William  Packard, 
Lot  Pool. 

Joseph  Richards, 
John  Redman, 
Wyatt  Richards, 
Alanson  Rice. 

Edward  Shaw, 
Zephaniah  Sampson, 
Franklin  Sawyer, 
Asa  Swallow, 
James  S.  Savage, 
Amos  C.  Sanborn% 

Job  Turner, 
Joseph  Tilden. 

Charles  Wells, 
William  Wood, 
Mordecai  L.  Wallis, 
Richard  Wither  ell, 
Henry  Wood, 
Jeremiah  Wetherbeey 
Salmon  Washburn* 


CHAPTER  II. 


SECTION  I.  Clay. 

The  substances  included  under  this  term,  are  mixtures  of  silex? 
or  the  ingredient  of  the  common  Gun  flint,  andalumine;  they  some- 
times contain  other  earths,  or  metallic  oxides,  by  the  latter  of  which, 
some  varieties  are  highly  colored.  Their  hardness  is  never  great  ; 
they  are  easily  cut  by  a  knife,  may  in  general  be  polished  by  fric- 
tion with  the  finger  nail,  and  are  usually  soft  to  the  touch.  When 
immersed  in  water,  they  crumble  more  or  less  readily,  and  become 
minutely  divided.  Many  clays,  when  moistened,  yield  a  peculiar 
odor,  called  argillaceous  ;  but  this  quality  appears  to  be  owing  to 
the  presence  of  metallic  oxides,  as  perfectly  pure  clays  do  not 
possess  it. 

The  substances  which  are  properly  termed  clays  may,  by  a  due 
degree  of  moisture  and  proper  management,  be  converted  into  a 
paste  more  or  less  tenacious  and  ductile,  which  constitutes  the  basis 
of  several  kinds  of  Pottery.  It  possesses  a  greater  or  less  degree  of 
unctuosity,  and  is  capable  of  assuming  various  forms  without  break- 
ing. This  argillaceous  paste,  when  dried  becomes  in  some  degree 
hard  and  solid,  and  by  exposure  to  a  sufficient  degree  of  heat,  may 
be  made  to  assume  a  stony  hardness. 

Clays  have  a  strong  affinity  for  water  ;  hence  the  avidity,  with 
which  they  imbibe  it  ;  hence  also,  they  adhere  more  or  less  to  the 
tongue  or  lips. 

Clay,  when  composed  of  only  silex  and  alumine,  in  any  propor- 
tions, is  infusible  in  a  furnace,  and  even  when  somewhat  impure,  it 
resists  a  degree  of  heat  without  melting.  But  the  presence  of  other 
earths,  particularly  of  lime,  or  of  a  large  quantity  of  oxide  of  iron 
with  a  little  lime  renders  it  fusible.  By  exposure  to  heat,  it  dimin- 
ishes in  bulk,  and  loses  somewhat  of  its  weight  by  the  escape  of 
water. 

Although  clay  is  essentially  composed  of  silex  and  alumine,  these 
ingredients  exist  in  various  proportions.  In  most  cases  silex  pre- 
dominates, being  in  the  proportion  of  two,  three,  or  even  four  parts 
to  one  of  alumine  ;  sometimes  the  proportions  are  nearly  equal,  and 
in  some  cases  the  alumine  predominates.  The  power  of  alumine  to 
impress  its  character  on  the  compound,  although  present  in  less  pro- 
portion than  the  silex,  probably  arises  from  a  greater  minuteness  of 
its  particles. 


46 


OPERATIVE  MASONRY. 


The  color  of  clay  may  proceed  from  oxide  of  iron,  or  from  some 
bituminous  or  vegetable  matter.  Hence  some  colored  clays,  when 
exposed  to  heat,  become  white  by  the  destruction  of  their  combus- 
tible ingredients,  while  others  suffer  merely  a  change  of  color,  by 
the  action  of  oxigen  on  the  iron.  The  purer  clays  are  white,  or 
gray,  and  suffer  little  or  no  change  by  the  action  of  fire. 

The  varieties  of  clay  are  numerous  ;  the  purest  kinds  are  exten- 
sively used  in  the  manufacture  of  porcelain  ware  ;  and  those  that 
are  less  pure  are  burnt  into  stone  ware  and  bricks. 

The  common  clays  may  be  divided,  in  regard  to  their  utility, 
into  three  classes.    The  Unctuous,  Meagre,  and  Calcareous. 

The  unctuous  contains,  in  general,  more  alumine  than  the  mea- 
gre, and  the  siliceous  ingredient  is  in  finer  grains  ;  when  burnt  it 
adheres  strongly  to  the  tongue,  but  its  texture  is  not  visibly  porous. 
When  containing  little  or  no  oxide  of  iron,  it  burns  to  a  very  good 
white  color,  and  is  very  infusible  ;  pipes  are  made  of  it,  and  it 
forms  the  basis  of  the  white  Staffordshire  ware.  If  it  contains  oxide 
of  iron,  sufficient  to  color  it  red,  when  baked,  it  becomes  much 
more  fusible,  and  can  only  be  employed  in  manufacturing  the 
coarser  kinds  of  pottery. 

Meagre  clay  is  such,  as,  when  dry,  does  not  take  a  polish  from 
rubbing  it  with  the  nail ;  it  feels  gritty  between  the  teeth,  and  the 
sand  which  it  contains  is  in  visible  grains.  When  burnt  without 
addition,  it  has  a  coarse  granular  texture,  and  is  employed  in  the 
manufacture  of  bricks  and  tiles. 

Calcareous  clay  effervesces  with  acids,  is  unctuous  to  the  touch, 
and  always  contains  iron  enough  to  give  it  a  red  color  when  baked. 
It  is  much  more  fusible  than  any  of  the  preceding  kinds,  and  is  only 
employed  in  brick-making.  By  judicious  burning  it  may  be  made 
to  assume  a  semi-vitrous  texture,  and  bricks  thus  made  are  very 
durable. 

Clays  are  very  abundant  in  nature,  and  contribute  the  most  to 
the  wants  and  conveniences  of  man,  of  all  the  earthy  minerals. 


SECTION  II.  Brick-Making. 

The  clay  for  the  purpose  of  making  bricks,  should  be  dug  in  the 
autumn ,  and  piled  in  solid  heaps.  During  the  winter  it  should  be 
broken  up,  and  exposed  in  such  masses,  from  day  to  day,  as  to  be- 
come thoroughly  penetrated  by  the  frost. 

In  the  spring,  the  clay  is  to  be  broken  into  small  pieces,  and  shov- 
elled over,  in  order  to  expel  the  frost.  After  this  is  done,  it  is 
thrown  into  pits  and  mixed  with  fine  sand  and  a  suitable  proportion 
of  water  :  the  sand  should  be  clear,  free  from  lumps  of  marl  and  si- 
line  particles;  siliceous  sand  is  to  be  preferred,  and  the  water  must 
be  fresh.  The  ingredients  are  to  be  worked  over  by  the  means  of 
the  shovel,  treading,  or  the  wheel,  till  they  are  properly  incorpo- 
rated, and  are  of  a  suitable  consistency  ; — in  this  way  they  are  pre- 
pared for  the  striker's  bench. 


OF  BRICK-MAKING. 


47 


In  preparing  for  a  brick-yard,  the  surface  of  the  ground  should 
be  cleared,  and  levelled  ;  a  coat  of  sand,  two  or  three  inches  in 
depth,  is  to  be  put  upon  it,  and  rendered  as  hard,  and  as  smooth  as 
is  practicable,  by  passing  a  heavy  roller  several  times  over  it  when 
wet.  After  this,  a  thin  layer  of  sand  is  sifted  upon  the  surface,  and 
a  wooden  scraper  passed  over  it,  in  order  to  render  it  as  smooth 
and  even  as  possible.  The  yard  should  be  of  a  size  sufficient  to 
contain  the  bricks  that  may  be  struck  in  two  days. 

Brick  moulds  are  commonly  made  to  contain  six  bricks  each. 
The  striker  is  prepared  with  two  moulds,  and  a  trough  of  water. 
When  the  prepared  clay  is  shovelled  on  to  the  striker's  table,  he 
takes  his  mould  from  the  trough  of  water,  adjusts  it  on  a  thin,  level 
board  bottom,  and  with  his  hands  wet,  to  prevent  adhesion,  strikes 
from  the  pile  of  mortar,  or  prepared  clay,  a  quantity  a  little  more 
than  sufficient  to  fill  one  of  the  apertures  of  the  mould,  which  he 
drops  into  it  with  considerable  force,  and  presses  it  firmly  down  ; 
he  then  strikes  the  surplus  off  with  his  hand,  and  thus  proceeds,  till 
all  the  apertures  of  the  mould  are  filled. 

A  second  person  (called  the  carrier)  now  takes  the  full  mould 
from  the  striker's  table,  to  another  part  of  the  brick-yard,  and  puts 
it  down  bottom  upwards.  The  bottom  board  is  then  drawn  off 
diagonally,  in  order  to  preserve  the  edges  of  the  bricks  entire  ;  the 
mould  is  raised,  and  the  bricks  left  on  the  sand  to  dry.  The  car- 
rier returns  the  empty  mould  to  the  striker's  trough,  takes  the  sec- 
ond full  mould  and  deposits  the  bricks  as  before.  The  bricks  are 
thus  exposed  in  ranges  till  they  are  so  dry  as  not  to  be  easily  defaced  ; 
they  are  then  placed  upon  their  edges  and  remain  till  they  are  dry 
enough  to  be  put  into  hacks.  The  hacks  are  composed  of  alternate 
layers  of  bricks,  the  first  layer  is  called  stretcher,  and  the  second  he- 
der;  interstices,  or  spaces  are  left  between  the  bricks  from  3-8  to  1-2 
an  inch,  so  that  the  air  may  have  a  free  circulation  between  them. 

The  bricks  ought  to  remain  in  this  situation  till  they  are  dry 
enough  to  go  into  the  kiln,  or  at  least,  for  six  or  eight  weeks  of 
dry  weather.  The  hacks  may  be  of  the  thickness  of  three  or  four 
bricks  placed  lengthwise,  and  six  or  eight  feet  in  height.  They  are 
to  be  protected  from  storms  by  sheds  erected  for  the  purpose. 

In  forming  bricks  into  a  kiln,  they  are  laid  in  benches,  with  arches, 
or  apertures  for  the  fuel.  A  bench  is  formed  in  this  manner.  Courses 
brick,  or  the  stretchers,  are  laid  lengthwise  ;  and  across  the  stretch- 
ers, or  at  right  angles  with  them,  are  laid  other  courses,  or  heders, 
interstices  are  left  between  the  bricks  from  1-4  to  1-2  of  an  inch  in 
thickness.  The  stretchers  and  heders  alternate  with  each  other  ;  and 
four  courses  of  them  form  a  bench.  Between  every  two  benches, 
there  is  a  space  left,  two  brick's  length  in  breadth,  for  arches.  The 
arches  are  formed  by  the  gradual  projection  of  the  courses  in  the  two 
benches,  about  as  far  as  the  eighth  course,  where  the  courses  of  the 
benches,  on  each  side  of  the  space,  meet,  at  the  distance,  generally,  of 
thirty-two  inches  from  the  ground.  The  benches  are  commonly 
raised  to  the  height  of  seven  or  eight  feet.  Thus  the  benches  and 
arches  alternate  with  each  other,  till  the  number  is  increased,  as  it 
may  be  deemed  expedient.  The  bricks  in  the  bench  are  placed  on 
their  edges,  and  care  should  be  taken  to  preserve  throughout  the 
7 


48 


OPERATIVE  MASONRY. 


interstices  between  their  sides,  so  that  the  heat  may  percolate.  At 
the  top  of  the  kiln,  the  outside  walls  should  have  an  inclination 
inwards,  of  about  one  foot  in  seven  of  perpendicular  height.  The 
kiln  is  faced  by  refuse  or  unburnt  bricks,  laid  up  in  clay  mortar, 
extending  around  the  whole  exterior  of  the  kiln,  the  thickness  of 
the  width  of  a  single  brick.  The  mouths  of  the  arches  are  to  be 
left  open,  and  flat  stones  prepared  for  closing  them,  while  the  kiln 
is  in  the  progress  of  burning. 

The  moulds  used  in  the  vicinity  of  Boston  are  commonly  8,  3-8 
inches  in  length,  2,  1-8  in  thicknes,  and  4,  1-2  in  width  ;  and 
bricks,  when  burnt,  vary  from  8  to  7,  3-4  inches  in  length,  and  are 
about  4  inches  in  width,  and  2  in  thickness,  according  to  the  length 
of  time,  and  the  degree  of  heat,  to  which  they  have  been  exposed. 

The  burning  is  commenced  with  a  moderate  heat,  in  order  first 
to  expel  the  moisture.  When  this  is  done,  the  smoke  changes  from 
a  great  degree  of  blackness  to  a  thin  transparent  glimmering. 

Then  the  intensity  of  the  heat  is  increased  to  as  great  a  degree, 
as  the  material  will  bear,  without  being  fused,  which  is  continued 
till  a  contraction,  or  shrinkage,  takes  place  at  the  top  of  the  kiln,  and 
at  the  ends  of  the  arches  opposite  to  those  in  which  the  fuel  is 
placed.  When  this  is  the  case,  it  is  necessary  to  close  the  mouths 
of  the  arches,  at  which  the  fuel  has  been  inserted,  and  to  put  it  in  at 
the  mouths  opposite.  At  the  close  of  the  process  of  burning,  the 
arches  are  filled  with  hard  wood  and  then  closed,  and  the  kiln  is  suf- 
fered to  remain  thus,  till  the  bricks  are  sufficiently  cool  for  hand- 
ling, before  they  are  exposed  to  the  air. 

A  machine  has  recently  been  been  patented,  and  put  in  operation 
in  this  vicinity,  for  preparing  the  materials  for  brick,  which  seems 
to  possess  many  advantages  over  the  common  method.  The  ma- 
chine consists  of  a  wheel  for  mixing  the  mortar,  and  apparatus  for 
filling  the  moulds,  and  is  worked  by  horse  or  steam  power.  It  posses- 
ses, among  others,  the  following  advantages;  that  of  pulverizing  the 
clay  more  thoroughly,  and  producing  a  more  homogeneous  and  com- 
pact paste,  and  in  consequence  the  bricks  are  less  liable  to  crack  in  the 
operation  of  drying,  or  burning  ;  and  by  being  more  firmly  pressed 
into  the  moulds,  they  are  less  liable  to  absorb  moisture  from  the  at- 
mosphere, and  are  rendered  smoother;  and  as  less  water  is  required 
by  this  mode,  in  making  the  paste,  the  bricks  do  not  require  the 
same  length  of  time  in  drying,  while  they  are  subject  to  shrink  less 
in  burning,  than  in  the  common  method.  And  lastly,  much  time 
and  labor  are  saved  in  the  operation. 


SECTION  III.  -Faced  or  Pressed  Bricks. 

These  bricks  are  used  to  form  the  facing  of  walls  in  the  better 
kind  of  structures,  and  are  finished  in  a  machine.  The  roughness 
and  change  of  form,  to  which  common  bricks  are  liable,  is  owing, 
in  part,  to  the  evaporation  of  a  portion  of  the  water  which  the  clay 
contains.    To  remedy  the  difficulty  arising  from  this  cause,  the 


FACED  OR  PRESSED  BRICKS. 


49 


bricks,  after  being  moulded  in  the  common  manner,  are  exposed  to 
the  sun  till  they  are  nearly  dried,  retaining  however,  sufficient  plas- 
ticity to  be  still  capable  of  a  slight  change  of  form.  The  moulds, 
however,  are  somewhat  larger  than  those  of  the  common  bricks, 
in  order  that  the  bricks,  when  pressed,  may  be  of  a  sufficient  size* 
The  press  machine  is  usually  made  of  cast-iron,  and  contains  a  num- 
ber of  moulds  arranged  in  a  circle,  or  otherwise,  so  that  the  power 
is  applied  to  them  in  succession,  and  the  bricks  pressed  with  rapidi- 
ty. The  mould  is  of  sufficient  thickness  to  resist  about  a  ton's 
weight,  applied  to  the  top  of  a  follower.  The  follower  is  fitted  as 
near  as  practicable,  to  the  inner  side  of  the  mould,  and  kept  in  a 
proper  position  to  be  forced  through,  when  the  moulds  are  removed 
from  their  beds.  This  is  done  by  the  means  of  a  wheel,  or  slide,  to 
which  the  mould  is  attached.  The  bricks,  being  pressed,  are  re- 
ceived on  a  carrying  board. 

The  force  is  applied  for  pressing  the  bricks,  by  the  means  of  a 
double  purchase  lever,  or  by  the  revolution  of  a  wheel  with  rollers 
running  on  an  oblique  plane. 

In  this  manner  about  five  thousand  bricks  may  be  pressed  off  in 
a  day,  by  the  labor  of  two  men  and  a  horse. 

The  pressed  bricks  are  of  a  superior  quality  in  point  of  durability 
and  elegance.    They  form  a  wall  with  a  surface  of  great  smooth- 
ness, and  when  carefully  laid,  produce  a  pleasing  effect.  These 
bricks  are  durable  from  their  hardness  and  smoothness,  being  less 
•    liable  to  decomposition  from  the  action  of  the  atmosphere. 

A  patent  was  obtained  in  England,  about  the  year  1795,  by  Mr. 
Cart wright,  for  an  improved  system  of  making  bricks  ;  of  which  the 
following  extract  will  furnish  all  necessary  information. 

"  Imagine  a  common  brick,  with  a  groove  on  each  side  down  the 
middle,  rather  more  than  half  the  width  of  the  side  of  the  brick  ; 
a  shoulder  will  thus  be  left  on  each  side  of  the  groove,  each  of 
which  will  be  nearly  equal  to  one  quarter  of  the  width  of  the  side  of 
the  brick,  or  to  one  half  of  the  groove,  or  rebate.  A  course  of  these 
bricks  being  laid  shoulder  to  shoulder,  they  will  form  an  indented 
line  of  nearly  equal  divisions,  the  grooves  being  somewhat  wider 
than  the  adjoining  shoulders,  to  allow  for  the  mortar  or  cement. 
When  the  second  course  is  laid  on,  the  shoulders  of  the  bricks, 
which  compose  it,  will  fall  into  the  grooves  of  the  first  course,  and 
the  shoulders  of  the  first  course  will  fit  into  the  grooves  of  the  sec- 
ond, and  so  with  every  succeeding  course.  Buildings  constructed 
with  these  bricks  will  require  no  bond  timbers,  as  an  universal  bond 
runs  through  the  whole  building,  and  holds  all  the  parts  together  ; 
the  walls  of  which  will  neither  crack  nor  bilge  without  breaking 
through  themselves.  When  bricks  of  this  construction  are  used  for 
arches,  the  sides  of  the  grooves  should  form  the  radii  of  a  circle,  of 
which  the  intended  arch  is  a  segment.  In  arch  work,  the  bricks 
may  either  be  laid  in  mortar,  or  dry,  and  the  interstices  afterwards 
filled  up  by  pouring  in  lime,  putty,  plaster  of  Paris,  &c.  Arches  of 
this  kind,  having  any  lateral  pressure,  can  neither  expand  at  the 
foot,  or  spring  at  the  crown,  consequently  they  need  no  abutments  ; 
neither  will  they  need  any  superincumbent  weight  on  the  crown,  to 
prevent  them  from  springing  up.    The  centres  may  also  be  struck 


50 


OPERATIVE  MASONRY. 


•  immediately,  so  that  the  same  centre,  which  never  need  be  many- 
feet  wide,  may  be  regularly  shifted  as  the  work  proceeds.  But  the 
most  striking  advantage  attending  this  invention,  is,  the  security  it 
affords  against  fire  ;  for,  from  the  peculiar  properties  of  this  kind  of 
arch,  requiring  no  abutments,  it  may  be  laid  upon,  or  let  into  com- 
mon walls,  no  stronger  than  what  are  required  for  timbers,  so  as  to 
admit  of  brick  floorings." 


SECTION  IV. 

The  use  of  bricks  in  building,  may  be  traced  to  the  earliest  ages, 
and  they  are  found  among  the  ruins  of  almost  every  ancient  nation. 
The  earliest  edifices  of  Asia  were  constructed  of  bricks,  dried  in 
the  sun,  and  cemented  with  bitumen.  Of  this  material  was  built 
the  ancient  city  of  Nineveh.  The  walls  of  Babylon,  some  of  the 
ancient  structures  of  Egypt  and  Persia,  the  walls  of  Athens,  the  ro- 
tunda of  the  Pantheon,  the  temple  of  Peace,  and  the  Thermae  at 
Rome,  were  all  of  brick.  The  earliest  bricks  were  never  exposed 
to  great  heat,  as  appears  from  the  fact,  that  they  contain  reeds  and 
straw,  upon  which  no  mark  of  burning  is  visible.  These  bricks 
owe  their  preservation  to  the  extreme  dryness  of  the  climate  in 
which  they  remained,  since  the  earth  of  which  they  were  made 
often  crumbles  to  pieces  when  immersed  in  water,  after  having  kept 
its  shape  for  more  than  two  thousand  years.  This  is  the  case  of 
some  of  the  Babylonian  bricks,  with  inscriptions  in  the  arrow  head- 
ed character,  which  have  been  brought  to  this  country.  The  an- 
cients, however,  at  a  later  period,  burnt  their  bricks,  and  it  is  these 
chiefly,  which  remain  at  the  present  day.  The  antique  bricks  were 
larger  than  those  employed  by  the  moderns,  and  were  almost  uni- 
versally of  a  square  form.  Those  of  Rome  appear  to  have  been  of 
three  different  sizes — the  largest  were  about  22  inches  square,  and 
2  1-4  inches  thick  ;  the  second  size  16  1-2  inches  square,  and  from 
1  1-2  to  2  inches  thick  ;  the  smallest  size  about  7  1-2  inches  square, 
and  11-2  thick.  In  order  to  secure,  more  effectually,  the  facing 
with  rubble,  the  Romans  placed  in  their  walls,  at  intervals  of  every 
three  or  four  feet,  two  or  three  courses  of  the  larger  brick,  (see  plate 
35,  Jig.  6.)  The  larger  bricks  were  used  in  the  formation  of  arches, 
and  in  the  openings  of  buildings. 

The  bricks  of  the  Greeks  were  commonly  cubical,  and  of  differ- 
ent sizes.  One  size  was  a  foot  on  all  sides  ;  another  kind  fifteen 
inches  ;  the  former  was  chiefly  used  in  the  construction  of  private, 
and  the  latter  in  public  edifices.  There  was  a  third  kind,  a  foot 
square,  and  six  inches  thick,  and  a  fourth  kind  fifteen  inches  square, 
and  seven  and  a  half  inches  thick  ;  these  two  last  kinds  were  called 
half  bricks,  and  were  used  for  the  purpose  of  better  effecting  the 
construction  of  a  bond,  (see  plate  34,  Jig.  4.)  They  also  employed, 
as  well  as  the  Romans,  another  size,  for  ornamental  walls,  called 
net  work,  (see  plate  35,  Jig.  7.)  This  net  work  had  a  beautiful  ap- 
pearance, but  was  liable  to  crack  ;  in  consequence,  according  to 


TILES. 


51 


Palladio,  there  are  no  ancient  specimens  of  this  kind  remaining. 
Vitruvius,  however,  states  the  form  of  these  bricks  to  have  been  a 
parallelogram,  six  inches  wide,  and  from  twelve  to  twenty-four 
inches  long. 

The  baked  bricks  of  the  ancients  were  generally  made  of  two 
parts  of  earth  and  one  of  cinders,  well  tempered  together.  They 
were  taken  from  the  moulds,  and  left  to  dry  in  the  sun  for  several 
days,  and  afterwards  placed  in  a  large  furnace,  ranged  one  over 
another,  at  some  distance  apart;  the  spaces  between  were  filled  with 
plaster,  or  a  sort  of  strata  of  fine  coal. 

Besides  bricks  made  of  clay,  the  ancients  also  employed  a  kind  of 
factitious  stone,  composed  of  a  calcareous  mortar.  They  were  also 
in  the  habit  of  using  bricks  and  stones,  both  rubble  and  wrought, 
in  the  same  wall. 

In  a  rubble  wall,  three  courses  of  bricks  were  laid  at  intervals  of 
two  or  three  feet,  for  the  purpose  of  binding  the  mass  together  ;  the 
angles  were  also  supported  by  piers  of  stone  or  bricks,  (see  plate  35, 

fig-  5«) 

In  buildings  of  more  magnificence,  (see  plate  35,  fig.  6,)  the  rubble 
was  concealed  in  the  wall.  The  bottom  of  the  wall  was  formed  of 
six  courses  of  large  bricks,  then  courses  of  smaller  bricks  were  laid 
up  to  the  height  of  three  feet.  Then  the  wall  was  bound  again 
with  three  courses  of  large  bricks,  and  so  on.  Examples  of  this 
kind  of  wall  still  remain  in  the  pantheon,  and  warm  baths  of  Di- 
oclesian. 


SECTION  V.  Tiles. 

Tiles  are  plates  of  burnt  clay,  resembling  bricks  in  their  compo- 
sition, and  manufacture,  and  used  for  the  covering  of  roofs.  They 
are  necessarily  made  thicker  than  slates,  or  shingles,  and  thus  im- 
pose a  greater  weight  upon  the  roofs.  Their  tendency  to  absorb 
water,  promotes  the  decay  of  the  wood  work  beneath  them. 

Tiles  are  usually  shaped  in  such  a  manner  that  the  edge  of  one 
tile  receives  the  edge  of  that  next  to  it,  so  that  water  cannot  perco- 
late between  them.  Tiles,  both  of  burnt  clay  and  marble,  were 
used  by  the  ancients,  and  the  former  continue  to  be  employed  in 
various  parts  of  Europe.  Floors,  made  of  fiat  tiles,  are  used  in  many 
countries,  particularly  in  France  and  Italy. 


SECTION  VI.  Compact  Lime-Stone. 

The  uses  and  geological  characters  of  this  substance,  render  it  pe- 
culiarly interesting.  The  term  compact,  however,  as  applied  to 
this  stone,  must  be  received  with  some  latitude  ;  for,  although  its 
texture  is  often  very  close  and  compact,  sometimes  like  that  of 
wax,  yet,  in  other  instances,  it  is  loose  and  earthy. 


52 


OPERATIVE  MASONRY. 


Among  the  numerous  colors  of  compact  lime-stone,  the  most  fre- 
quent are  the  various  shades  of  gray,  such  as  smoke-gray,  yellowish 
gray,  bluish  gray,  reddish  and  greenish  gray  ;  it  is  also  seen  gray- 
ish white,  grayish  black  ;  flesh  red,  with  some  deep  tints  of  red  and 
yellow  ;  several  of  these  colors  often  occur  in  the  same  fragment, 
which  are  distinguished  by  the  epithet  of  marbled. 

It  usually  occurs  in  extensive,  solid,  compact  masses,  whose  frac- 
ture is  dull  and  splintery,  or  even,  and  sometimes  conchoidal. 
It  is  sometimes  traversed  by  minute  veins  of  calcareous  spar, 
which  reflect  a  little  light  ;  and  some  compact  lime-stones  are 
also  slaty.  Its  hardness  is  somewhat  variable.  Its  specific  gravity 
usually  lies  between  2.  40  and  2.  75.  It  is  opaque,  and  more  or  less 
susceptible  of  a  polish. 

Compact  lime-stone  is  seldom,  perhaps  never,  a  pure  carbonate  ; 
but  contains  from  2  to  12  per  cent,  of  silex,  alumine,  and  the  oxide 
of  iron,  on  the  last  of  which  its  diversified  colors  depend.  In  fact, 
by  increasing  the  proportion  of  argillaceous  matter,  it  passes  into 
marl.  Some  lime-stones,  which  effervesce  considerably  with  an 
acid,  are  still  so  impure,  that  they  melt  rather  than  burn  into  lime. 

The  uses,  to  which  compact  lime-stone  is  applied,  are  various  ; 
it  is  principally  employed  as  a  building  stone,  and  burnt  for  making 
lime  and  mortar  ;  nor  is  it  less  important  to  the  agriculturist  as  a 
manure,  to  the  miner  as  a  flux,  for  the  reduction  of  ores,  to  the 
soap-boiler,  to  the  tanner,  &c.  It  is  a  substance  very  abundantly  dif- 
fused throughout  the  globe. 

It  is  from  compact  lime-stone,  that  lime,  so  extensively  used  in  the 
arts,  is  chiefly  obtained  ;  pure  white  marble,  or  lime-stone,  undoubt- 
edly furnishes  the  best  lime,  though  but  little  superior  to  that  ob- 
tained from  gray,  compact  lime-stone. 


SECTION  VII.  The  Burning  of  Lime. 

This  is  a  process  by  which  lime-stone,  marble,  shells,  &c,  are  con- 
verted into  lime,  by  means  of  heat,  in  kilns  properly  constructed  for 
the  purpose.  By  the  application  of  heat,  to  any  of  these  substances, 
their  carbonic  acid  is  driven  off,  and  leaves  the  lime  in  a  powder. 

The  calcination  of  lime-stone  may  be  effected  by  wood,  coal,  or 
peat,  as  fuel  ;  but  the  heat  should  not  much  exceed  a  red  heat,  un- 
less the  stone  employed  be  nearly  a  pure  carbonate.  The  fuel  is 
placed  in  layers,  alternately  with  those  of  the  stones,  or  calcareous 
materials  in  the  kilns,  and  the  process  of  burning  continued  for 
any  length  of  time,  by  repeated  applications  of  fuel  and  the  calcare- 
ous materials  at  the  top  ;  the  lime  being  drawn  out  occasionally 
from  below,  as  it  is  burnt. 

Fossil,  or  mineral  coal,  are  supposed  to  be  the  most  convenient  and 
suitable  materials  for  effecting  this  business,  where  they  can  be  pro- 
cured plentifully,  and  at  a  sufficiently  cheap  rate  ;  as  they  burn  the 
stone,  or  other  calcareous  matter  more  perfectly,  and,  of  course, 
leave  fewer  cores  in  the  calcined  pieces,  than  when  other  sorts  of 
fuel  are  employed  for  the  purpose. 


COMMON  MORTAR  AND  CEMENT. 


53 


Peat,  also,  is  highly  recommended  for  its  cheapness  and  uni- 
formity of  heat.  When  coal  is  used,  the  lime-stones  are  liable,  from 
excessive  heat,  to  run  into  solid  lumps  ;  which  may  be  avoided  by  the 
use  of  peat,  as  it  keeps  them  in  an  open  state,  and  admits  the  air 
freely. 

Count  Rumford,  with  his  usual  attention  to  economy  in  fuel,  and 
in  the  expense  of  caloric,  has  invented  an  oven  for  preparing  lime. 
It  has  the  form  of  a  high  cylinder  with  a  hearth  at  the  side,  and  at 
some  distance  above  the  base.  The  combustible  is  placed  on  the 
hearth,  and  burns  with  an  inverted  or  reflected  flame.  The  lime  is 
taken  out  at  the  bottom,  while  fresh  additions  of  lime-stone  are  made 
at  the  top  ;  and  thus  the  oven  is  preserved  constantly  hot, 

Lime-stone  recently  dug,  and  of  course  moist,  calcines  more  easily 
than  that  which  has  become  dry  by  exposure  to  the  air:  in  the  lat- 
ter case  it  is  found  convenient  even  to  moisten  the  stone,  before  put- 
ting it  into  the  kiln. 

Lime-stone  loses  about  four-ninths  of  its  weight  by  burning  ;  but 
is  nearly  of  the  same  bulk. 

Lime  thus  obtained,  is  called  quick-lime.  If  it  be  wet  with  wa- 
ter, it  instantly  swells  and  cracks,  becomes  exceedingly  hot,  and  at 
length  falls  into  a  white,  soft,  impalpable  powder.  This  process  is 
denominated  the  slaking  of  lime.  The  compound  formed  is  called 
the  hydrate  of  lime,  and  consists  of  about  three  parts  of  lime  to  one 
of  water.  When  intended  for  mortar,  it  should  immediately  be  in- 
corporated with  sand,  and  used  without  delay,  before  it  imbibes 
carbonic  acid  anew  from  the  atmosphere.  Lime  doubles  its  bulk 
by  slaking. 


SECTION  VIII.  Common  Mortar  and  Cement. 

These  are  the  substances  generally  made  use  of,  for  the  uniting 
medium  between  bricks,  or  stones,  in  forming  them  into  buildings. 
Though  many  experiments  have  been  made  to  ascertain  the  best 
materials  for  these  compounds,  and  the  mode  of  mixing  them,  and 
not  without  a  degree  of  success,  still,  much  yet  seems  to  remain  to 
be  discovered.  A  composition  of  lime,  sand  and  water,  in  conse- 
quence of  the  facility,  with  which  they  pass  from  a  soft  state  to  a 
stony  hardness,  has,  in  common  uses,  superseded  all  other  ingredi- 
ents. But  in  order  that  the  mortar  should  be  of  a  good  quality, 
great  care  and  skill  are  requisite,  in  the  selection  of  the  materials, 
and  the  proportioning  of  them  ;  and  much  depends  on  the  degree  of 
labor  bestowed  on  the  mixing  and  incorporation.  The  lime  should 
be  well  burnt,  and  free  from  fixed  air  and  carbonic  acid.  Hence, 
lime  that  has  become  effete  from  exposure  to  the  atmosphere,  is  im- 
paired in  its  quality.  The  sand  most  proper  for  mortar  is  that 
which  is  wholly  siliceous,  and  which  is  sharp,  that  is,  not  having 
its  particles  rounded  by  attrition.  Fresh  sand  is  to  be  preferred  to 
that,  taken  from  the  vicinity  of  the  sea-shore,  the  salt  of  which  is 
liable  to  deliquesce  and  weaken  the  strength  of  the  mortar:  it 


54 


OPERATIVE  MASONRY. 


should  be  clean,  rather  coarse,  and  free  from  dirt  and  all  perishable 
ingredients.  The  water  should  be  pure,  fresh,  and,  if  possible,  free 
from  fixed  air. 

The  proportions  of  lime  and  sand  to  each  other,  are  varied  in 
different  places  ;  the  amount  of  sand,  however,  always  exceeds  that 
of  lime.  The  more  sand  that  can  be  incorporated  with  the  lime, 
the  better,  provided  the  necessary  degree  of  plasticity  is  preserved; 
for  the  mortar  becomes  stronger,  and  it  also  sets,  or  consolidates 
more  quickly,  when  the  lime  and  water  are  less  in  quantity  and 
more  subdivided.  From  two  to  four  parts  of  sand  are  commonly 
used  to  one  of  lime,  according  to  the  quality  of  the  lime,  and  the 
labor  bestowed  upon  it.  The  more  pure  the  lime  is,  and  the  more 
thoroughly  it  is  beaten,  or  worked  over,  the  more  sand  it  will  take 
up,  and  the  more  firm  and  durable  does  it  become. 


SECTION  IX. 

The  aneient  masons  were  so  very  scrupulous  in  the  process  of  mix- 
ing their  mortar,  that  it  is  said  the  Greeks  kept  ten  men  constantly 
employed  for  a  long  space  of  time,  to  each  bason;  this  rendered  their 
mortar  of  such  prodigious  hardness,  that  Vetruvius  tells  us,  the 
pieces  of  plaster  falling  off  from  old  walls,  served  to  make  tables. 

It  was  a  maxim  among  the  old  masons  to  their  laborers,  that  they 
should  dilute  the  mortar  with  the  sweat  of  their  brows,  that  is,  la- 
bor a  long  time,  instead  of  drowning  it  with  water  to  have  it  done 
the  sooner. 

The  weakness  of  modern  mortar,  compared  to  the  ancient,  is  a 
common  subject  of  regret  ;  and  many  ingenious  men  take  it  for 
granted,  that  the  process  used  by  the  Roman  architects  in  preparing 
their  mortar,  is  one  of  those  arts  which  is  now  lost,  and  have  em- 
ployed themselves  in  making  experiments  for  its  recovery. 

But  the  characteristics  of  all  modern  artists,  builders  among  the 
rest,  seems  to  be,  to  spare  their  time  and  labor  as  much  as  possible, 
and  to  increase  the  quantity  of  the  article  they  produce,  without 
much  regard  to  goodness  ;  and  perhaps  there  is  no  manufacture,  in 
which  it  is  so  remarkably  exemplified,  as  in  the  preparation  of  com- 
mon mortar. 


SECTION  X. 

Mr.  Doffie  gives  the  following  method  of  making  mortar  impen- 
etrable to  moisture,  acquiring  great  hardness,  and  exceedingly  du- 
rable, which  was  discovered  by  a  gentleman  of  Neufchatel.  Take 
of  unslacked  lime,  and  of  fine  sand,  in  the  proportion  of  one  part  of 
lime  to  three  of  sand,  as  much  as  a  laborer  can  well  manage  at  once; 
and  then,  adding  water  gradually,  mix  the  whole  well  together  with 


MONSIEUR  LORIAT'S  MORTAR.  55 

a  trowel,  till  it  be  rendered  to  the  consistency  of  mortar.  Apply  it 
immediately,  while  it  is  hot,  to  the  purpose,  either  of  mortar,  as  a 
cement  to  brick  or  stone,  or  of  plaster,  to  the  surface  of  any  build- 
ing. It  will  then  ferment  for  some  days  in  drier  places,  and  after- 
wards gradually  concrete,  or  set,  and  become  hard  ;  but  in  a  moist 
place,  it  will  continue  soft  for  three  weeks,  or  more  ;  though  it  will 
at  length  obtain  a  firm  consistence,  even  if  water  have  such  access 
to  it  as  to  keep  the  surface  wet  the  whole  time.  After  this  it  will 
acquire  a  stone-like  hardness,  and  resist  all  moisture.  The  perfec- 
tion of  this  mortar  depends  on  the  ingredients  being  thoroughly 
blended  together  ;  and  the  mixture  being  applied  immediately  after, 
to  the  place  where  it  is  wanted.  The  lime  for  this  mortar  must  be 
made  of  hard  lime-stone,  shells  or  marl ;  and  the  stronger  it  is,  the 
better  the  mortar  will  be.  When  a  very  great  hardness  and  firm- 
ness are  requisite  in  this  mortar,  the  using  of  skimmed  milk,  instead 
of  water,  either  wholly  or  in  part,  will  produce  the  desired  effect. 


SECTION  XI.  Monsieur  Loriat's  Mortar. 

Monsieur  LoriaVs  Mortar^ — The  method  of  making  which,  was 
announced  by  order  of  his  majesty,  at  Paris,  in  1774 :  it  is  made  in 
the  following  manner: — Take  one  part  of  brick  dust,  finely  sifted, 
two  parts  of  fine  river  sand,  screened,  and  as  much  old  slaked  lime 
as  may  be  sufficient  to  form  mortar  with  water,  in  the  usual  method, 
but  so  wet  as  to  serve  for  the  slaking  of  as  much  powdered  quick- 
lime as  amounts  to  one  fourth  of  the  whole  quantity  of  brick-dust 
and  sand.  When  the  materials  are  well  mixed,  employ  the  compo- 
sition quickly,  as  the  least  delay  may  render  the  application  im- 
perfect, or  impossible.  Another  method  of  making  this  compound 
is,  to  make  a  mixture  of  the  dry  materials;  that  is,  of  the  sand,  brick- 
dust,  and  powdered  quick-lime,  in  the  prescribed  proportion  ;  which 
mixture  may  be  put  into  sacks,  each  containing  a  quantity  sufficient 
for  one  or  two  troughs  of  mortar.  The  above  mentioned  old  slaked 
lime  and  water  being  prepared  apart,  the  mixture  is  to  be  made  in 
the  manner  of  plaster,  at  the  instant  when  it  is  wanted,  and  is  to  be 
well  chafed  with  the  trowel. 


SECTION  XII. 

Dr.  Higgins  has  made  a  variety  of  experiments,  in  consequence 
of  the  modern  discoveries  relating  to  fixed  air,  for  the  purpose  of 
improving  the  mortar  used  in  buildings.  According  to  this  author, 
the  perfection  of  lime,  prepared  for  the  purpose  of  making  mortar, 
consists  cheifly  in  its  being  totally  deprived  of  its  fixed  air.  And 
as  lime  very  quickly  imbibes  fixed  air,  when  exposed  to  the  atmos- 
phere, it  should  be  applied  to  use  as  soon  as  possible  after  it  is  pre- 
pared. 

8 


56 


OPERATIVE  MASONRY. 


From  the  experiments  of  the  same  author,  made  with  a  view  to 
ascertain  the  best  relative  proportions  of  lime,  sand,  and  water,  in 
the  making  of  mortar,  it  appeared  that  those  specimens  were  the 
best,  which  contained  one  part  of  lime  in  seven  of  sand  ;  for  those 
which  contained  less  lime,  and  were  too  short  while  fresh,  were 
more  easily  cut  and  broken,  and  were  pervious  to  water ;  and  those 
which  contained  more  lime,  although  they  were  closer  in  grain,  did 
not  harden  so  soon,  or  to  so  great  a  degree,  even  when  they  escaped 
cracking  by  lying  in  the  shade  to  dry  slowly. 

Dr.  Higgins  has  also  shown,  that  though  the  setting  of  mortar,  as 
it  is  called,  is  chiefly  owing  to  its  drying,  yet  its  induration,  or  its 
acquiring  a  stony  hardness,  is  not  caused  by  its  drying,  as  has  been 
supposed,  but  depends  principally  on  its  acquiring  carbonic  acid,  or 
fixed  air,  from  the  atmosphere.  In  order  to  the  greatest  induration 
of  mortar,  therefore,  it  must  be  suffered  to  dry  gently,  and  set ;  the 
drying  must  be  effected  by  temperate  air,  and  not  accelerated  by 
the  heat  of  the  sun,  or  fire.  It  must  not  be  wet  soon  after  it  sets  ; 
and  afterwards,  it  ought  to  be  protected  from  wet  as  much  as  possi- 
ble, until  it  is  completely  indurated.  The  same  author  describes  a 
cement,  or  stucco,  of  his  own  invention,  for  incrustations,  external 
and  internal,  of  very  great  hardness,  for  which  he  obtained  letters 
patent.  As  for  the  materials  of  which  it  is  made,  drift  sand,  or 
quarry  sand,  consisting  chiefly  of  hard  quartose  flat-faced  grains,  with 
sharp  angles,  free  from  clay,  salts,  &c.  is  to  be  preferred.  The  sand 
is  to  be  sifted  in  streaming  clear  water,  through  a  sieve  which  shall 
give  passage  to  all  such  grains  as  do  not  exceed  one  sixteenth  of  an 
inch  in  diameter  ;  and  the  stream  of  water,  and  sifting,  are  to  be  so 
regulated,  that  all  the  finer  sand,  together  with  clay  and  other  mat- 
ter lighter  than  sand,  may  be  washed  away  with  the  stream. 
While  the  purer  and  coarser  sand,  which  passes  through  the  sieve, 
subsides  in  a  convenient  receptacle,  the  coarse  rubbish  in  the  sieve 
is  to  be  rejected.  The  subsiding  sand  is  then  washed  in  clean 
streaming  water,  through  a  finer  sieve,  so  as  to  farther  cleanse  it, 
and  sorted  into  two  parcels, — a  coarser,  which  will  remain  in  the 
sieve,  which  is  to  give  passage  only  to  such  grains  as  are  less  than 
one  thirteenth  of  an  inch  in  diameter,  and  which  is  to  be  kept  apart 
under  the  name  of  coarse  sand  ;  and  a  finer,  which  will  pass  through 
the  sieve,  and  subside  in  the  water,  and  which  is  to  be  saved  apart 
under  the  name  of  fine  sand.  These  are  to  be  dried  separately, 
either  in  the  sun,  or  on  a  clean  iron  plate  set  on  a  convenient  surface, 
in  the  manner  of  a  sand  heat.  The  lime  to  be  chosen,  should  be 
stone-lime,  which  heats  the  most  in  slaking,  and  slakes  the  quickest 
when  duly  watered  ;  which  is  the  freshest  made,  and  most  closely 
kept.  Let  this  lime  be  put  into  a  brass-wired,  fine  sieve,  to  the 
quantity  of  fourteen  pounds.  Let  the  lime  be  slaked  by  plunging 
it  in  a  butt,  filled  with  soft  water,  and  raising  it  out  quickly,  and 
suffering  it  to  heat  and  fume,  and  by  repeating  this  plunging,  and 
raising  alternately,  and  agitating  the  lime,  until  it  be  made  to  pass 
through  the  sieve.  Reject  the  part  of  the  lime  that  does  not  easily 
pass  through  the  sieve,  and  use  fresh  portions  of  lime,  till  as  many 
ounces  have  passed  through  the  sieve  as  there  are  quarts  of  water  in 


METHOD  OF  MAKING  MORTAR.  57 

the  butt.  Let  the  water  thus  impregnated,  stand  in  the  butt,  close 
covered,  until  it  becomes  clear  ;  and  through  wooden  cocks,  placed 
at  different  heights  in  the  butt,  draw  off  the  clear  liquor,  as  fast  and 
as  low  as  the  lime  subsides,  for  use.  This  clear  liquor  is  called  the 
cementing  liquor. 

Let  fifty-six  pounds  of  the  aforesaid  chosen  lime  be  slaked,  by 
gradually  sprinkling  on  it  the  cementing  liquor,  in  a  close,  clean 
place.  Let  the  slaked  part  be  immediately  sifted  through  the  fine 
brass-wired  sieve.  Let  the  lime  which  passes  be  used  instantly,  or 
kept  in  air-tight  vessels,  and  let  the  part  of  the  lime  which  does 
not  pass  through  the  sieve  be  rejected ;  the  other  part  is  called  pu- 
rified lime. 

Let  bone-ashes  be  prepared  in  the  usual  manner,  by  grinding  the 
whitest  burnt  bones  ;  but  they  should  be  finely  sifted. 

Having  thus  prepared  the  materials,  take  fifty-six  pounds  of  the 
coarse  sand,  and  forty-two  pounds  of  the  fine  sand  ;  mix  them  on  a 
large  plank  of  hard  wood,  placed  horizontally.  Then  spread  the 
sand  so  that  it  may  stand  at  the  height  of  six  inches,  with  a  flat  sur- 
face on  the  plank  ;  wet  it  with  the  cementing  liquor  ;  to  the  wetted 
sand  add  fourteen  pounds  of  the  purified  lime,  in  several  successive 
portions,  mixing  and  beating  them  together  ;  then  add  fourteen 
pounds  of  the  bone  ashes  in  successive  portions,  mixing  and  beating 
them  all  together.  This,  Dr.  Higgins  calls  the  water  cement, 
coarse  grained,  which  is  to  be  applied  in  building,  pointing,  plas- 
tering, stuccoing,  &c.  Observing  to  work  it  expeditiously  in  all 
cases,  and  in  stuccoing,  to  lay  it  on  by  sliding  the  trowel  upwards 
upon  it  ;  to  well  wet  the  materials  used  with  it,  or  the  ground  on 
which  it  is  laid,  with  the  cementing  liquor,  at  the  time  of  laying  it 
on  ;  and  to  vise  the  cementing  liquor  for  moistening  the  cement  and 
facilitating  the  floating  of  it. 

A  cement  of  a  finer  texture  may  be  made,  by  using  ninety  pounds 
of  the  fine  sand,  and  fifteen  pounds  of  lime,  with  bone-ashes  and  ce- 
menting liquor.  This  is  called  water  cement,  fine  grained  ;  and  is 
used  in  giving  the  last  coating  or  finish  to  any  work,  intended  to 
imitate  the  finer  grained  stones  or  stucco. 

For  a  cheaper  or  coarser  cement,  take  of  coarse  sand,  fifty-six 
pounds,  of  the  foregoing  coarse  sand,  twenty-eight  pounds,  and  of 
the  finer  sand,  fourteen  pounds  ;  and  after  mixing  and  wetting 
these  with  the  cementing  liquor,  add  fourteen  pounds  of  the  puri- 
fied lime,  and  then  as  much  bone-ashes,  mixing  them  together. 
The  water  cement  above  described,  is  applicable  to  forming  artificial 
stone  ;  by  making  alternate  layers  of  the  cement  and  of  flint,  hard 
stone,  or  brick,  in  moulds  of  the  figure  of  the  intended  stone,  and 
by  exposing  the  masses  so  formed  to  the  open  air  to  harden.  When 
the  cement  is  required  for  water  fences,  two  thirds  of  the  bone-ash- 
es, are  to  be  omitted,  and  in  their  stead,  an  equal  measure  of  pow- 
dered terras  (see  Terras,)  is  to  be  used.  When  the  cement  is  requir- 
ed of  the  finest  grain,  or  in  a  fluid  form,  so  that  it  may  be  applied 
with  a  brush,  flint  powder,  or  the  powder  of  any  quartose,  or  hard 
earthy  substance,  may  be  used  in  the  place  of  sand,  so  that  the  pow- 


58 


OPERATIVE  MASONRY. 


der  shall  not  be  more  than  six  times  the  weight  of  the  lime,  nor  less 
than  four  times  its  weight.  For  inside  work  the  admixture  of  hair 
with  the  cement  is  useful. 

When  a  fragment  of  a  worked  stone,  is  by  accident,  or  otherwise, 
broken  off,  it  may  be  united,  with  a  firmness  sufficient  to  resist  a 
considerable  degree  of  force,  by  a  cement  made  of  5  parts  of  gum 
shelac,  and  1  part  of  Burgundy  pitch,  incorporated  together,  in  an 
iron  vessel,  over  a  slow  fire.  The  cement,  while  hot,  should  be  ap- 
plied to  the  stone,  raised,  also,  to  a  moderate  degree  of  heat.  In 
order  that  the  cement  should  not  cool  too  rapidly,  a  piece  of  iron 
should  be  heated,  and  laid  on  the  stone,  and  the  whole  suffered  to 
cool  gradually  together.  The  cement  may  be  made  to  assume  the 
color  of  the  stone  to  be  united,  by  mixing  with  it  a  portion  of  the 
stone  itself,  reduced  to  a  fine  powder.  Stones,  thus  united,  may 
afterwards  be  smoothed,  by  gentle  hammering,  while  the  fracture 
is  not  perceptible,  except  by  very  close  examination. 


SECTION  XIII. 

Although  a  well  made  mortar,  composed  merely  of  sand  and  lime, 
allowed  to  dry,  becomes  impervious  to  water,  so  as  to  serve  for 
the  lining  of  reservoirs  and  aqueducts  ;  yet  if  the  circumstances  of  the 
building  are  such  as  to  render  it  impracticable  to  keep  out  the  water, 
whether  fresh  or  salt,  a  sufficient  length  of  time,  the  use  of  common 
mortar  must  be  abandoned. 

Among  the  nations  of  antiquity,  the  Romans  appear  to  have  been 
the  only  people,  who  have  practised  building  in  water,  and  espe- 
cially in  the  sea,  to  any  extent.  The  bays  of  Baiae,  of  Pozzuoli  and 
of  Cumae,  from  their  coolness  and  salubrity  of  situation,  were  the 
fashionable  resorts  of  the  wealthier  Romans,  during  the  summer 
months;  who  not  only  erected  their  villas  and  baths  as  near  the  shore 
as  possible,  but  constructed  moles,  and  formed  small  islands,  in  the 
more  sheltered  parts  of  these  bays;  on  which,  for  the  sake  of  the  grate- 
ful coolness,  they  built  their  summer  houses  and  pavilions.  They 
were  enabled  to  build  thus  securely,  by  the  disco  very,  at  the  town 
of  Puteoli,  of  an  earthy  substance,  which  was  called  pulvis  puteolanus, 
Puteolan  powder,  or  as  it  is  now  called,  puzzolana,  (which  see) .  The 
only  preparation,  which  this  substance  undergoes,  is  that  of  pound- 
ing and  sifting,  by  which  it  is  reduced  to  a  coarse  powder  ;  in  this 
state,  being  thoroughly  beaten  up  with  lime,  either  with  or  without 
sand,  it  forms  a  mass  of  remarkable  tenacity,  which  speedily  sets, 
under  water,  and  becomes,  at  least,  as  hard  as  good  free-stone. 

Limes,  which  contain  a  portion  of  clay,  or  argillaceous  matter,  have 
also  the  property  of  forming  a  mortar,  which  hardens  under  water. 
A  composition,  formed  of  two  bushels  of  clayey  lime,  one  bushel  of 
puzzolana,  and  three  of  clean  sand,  the  whole  being  well  beaten  to- 
gether, make  a  good  water  cement. 


STUCCO. 


59 


The  Terras,  which  is  so  much  used  in  Holland,  is  a  preparation  of 
a  species  of  basalt,  (which  see,)  by  calcination.  It  possesses  the 
property,  when  mixed  with  lime,  of  forming  a  water  cement,  not 
inferior  to  puzzolana.  Perhaps  common  green-stone  and  other  sub- 
stances may  be  found  to  answer  the  same  purposes. 

The  materials  of  terras  mortar,  generally  used  in  the  construction 
of  the  best  water  work,  are  one  measure  of  quick-lime,  or  two 
measures  of  slaked  lime,  in  the  dry  powder,  mixed  with  one  measure 
of  terras,  well  beaten  together  to  the  consistency  of  paste,  using  as 
little  water  as  possible. 

Another  kind,  almost  equally  good,  and  considerably  cheaper,  is 
made  of  two  measures  of  slaked  lime,  one  of  terras,  and  three  of 
coarse  sand  ;  it  requires  to  be  beaten  longer  than  the  foregoing,  and 
produces  three  measures  and  a  half  of  excellent  mortar.  When  the 
building  is  constructed  of  rough,  irregular  stones,  where  cavities  and 
large  joints  are  to  be  filled  up  with  cement,  the  pebble,  or  coarse 
sand  mortar,  may  be  most  advantageously  applied  ;  this  was  a  favor- 
ite mode  of  constructing  among  the  Romans,  and  has  been  much 
used  since.  Pebble  mortar  will  be  found  of  a  sufficient  compact- 
ness, if  composed  of  two  measures  of  slaked,  argillaceous  lime,  half 
a  measure  of  terras,  or  puzzolana,  and  one  measure  of  coarse  sand} 
one  of  fine  sand,  and  four  of  small  pebbles,  screened  and  washed. 
It  is  only  under  water,  that  the  terras  mortar  sets  well. 

The  scales  produced  by  hammering  red-hot  iron,  which  may  be 
procured  at  the  forges  and  blacksmith's  shops,  have  been  long 
known  as  an  excellent  material  in  water  cements.  The  scales  being 
pulverized  and  sifted,  and  incorporated  with  lime,  are  found  to  pro- 
duce a  cement  equally  powerful  with  puzzolana  mortar,  if  employed 
in  the  same  quantity. 

Fresh  made  mortar,  if  kept  under  ground,  in  considerable  masses, 
may  be  preserved  for  a  great  length  of  time,  and  the  older  it  is  be- 
fore it  is  used,  the  better  it  has  been  thought  to  be. 

Pliny  imforms  us,  that  the  ancient  Roman  laws  prohibited  build- 
ers from  using  mortar  that  was  less  than  three  years  old  ;  and  a  sim- 
ilar law  prevails  in  Vienna. 


SECTION  XIV.  Stucco. 

This  is  a  composition  of  white  marble,  pulverized,  and  mixed 
with  plaster,  or  lime  ;  the  whole  sifted  and  wrought  up  with  water  ; 
to  be  used  like  common  plaster. 

Of  this  are  made  statues,  busts,  basso-relievos  and  other  ornaments 
of  architecture. 

\  stucco,  for  walls,  &c.  may  be  formed  of  the  grout,  or  putty, 
made  of  good  stone-lime,  or  the  lime  of  cockle  shells,  which  is  bet- 
ter, properly  tempered  and  sufficiently  beat,  mixed  with  sharp  grit 
sand,  in  a  proportion  which  depends  on  the  strength  of  the  lime. 
Drift-sand  is  best  for  this  purpose,  and  it  will  derive  advantage  from 


60 


OPERATIVE  MASONRY. 


being  dried  on  an  iron  plate  or  kiln,  so  as  not  to  burn,  thus  the  mor- 
tar would  be  discolored.  When  this  is  properly  compounded,  it 
should  be  put  in  small  parcels  against  walls,  or  otherwise  to  mellow, 
as  the  workmen  term  it  ;  reduced  again  to  soft  putty,  or  paste,  and 
spread  thin  on  the  walls  without  any  under  coat,  and  well  trowelled. 
A  succeeding  coat  should  be  laid  on,  before  the  first  is  quite  dry, 
which  will  prevent  points  of  brick  work  appearing  through  it. 
Much  depends  on  the  workman  giving  sufficient  labor,  and  trowel- 
ling it  down.  If  this  stucco,  when  dry,  be  laid  over  with  boiling 
linseed  oil,  it  will  last  a  long  time,  and  not  be  liable,  when  once 
hardened,  to  the  accidents  to  which  common  stucco  is  liable. 


SECTION  XV. 

Adam's  Oil  Cement,  or  Stucco,  is  prepared  in  the  following  manner. 
For  the  first  coat,  take  twenty-one  pounds  of  fine  whiting,  or  oyster- 
shells,  or  any  other  sea-shells  calcined,  or  plaster  of  Paris,  or  any 
calcareous  material  calcined  and  pounded,  or  any  absorbent  materials 
whatever,  proper  for  the  purpose  ;  add  white  or  red  lead  at  pleas- 
ure ;  deducting  from  the  other  absorbent  materials  in  proportion  to 
the  white  or  red  lead  added  ;  to  which  put  four  quarts,  beer  meas- 
ure, of  oil ;  and  mix  them  together  with  a  grinding-mill  or  any  lev- 
igating machine.  And  afterwards  mix,  and  beat  up  the  same  well 
with  twenty-eight  pounds,  beer  measure,  of  any  sand  or  gravel,  or 
of  both,  mixed  and  sifted,  or  of  marble  or  stone  pounded,  or  of  brick 
dust,  or  of  any  kind  of  metallic,  or  mineral  powders,  or  of  any  solid 
material  whatever,  fit  for  the  purpose. 

For  the  second  coat,  take  sixteen  pounds  and  a  half  of  superfine 
whiting,  or  oyster-shells,  or  any  sea-shells  calcined,  &c,  as  for  the 
first  coat  ;  add  sixteen  pounds  and  a  half  of  white  or  red  lead,  to 
which  put  six  quarts  and  a  half  of  oil,  wine  measure,  and  mix  them 
together  as  before.  Afterwards  mix  and  beat  up  the  same  well  with 
thirty  quarts,  wine  measure,  of  fine  sand  or  gravel,  sifted,  or  stone, 
or  marble  pounded,  or  pyrites,  or  any  kind  of  metallic  or  mineral 
powder,  &c.  This  composition  requires  a  greater  proportion  of  sand, 
gravel  or  other  solids,  according  to  the  nature  of  the  work,  or  the 
uses  to  which  it  is  to  be  applied.  If  it  be  required  to  have  the  com- 
position colored,  add  to  the  above  ingredients  such  a  portion  of 
painters'  colors  as  will  be  necessary  to  give  the  tint  or  color  required. 
In  making  the  composition,  the  best  linseed,  or  hemp  seed,  or  other 
oils,  proper  for  the  purpose,  are  to  be  used,  boiled  or  raw,  with 
drying  ingredients,  as  the  nature  of  the  work,  the  season,  or  the  cli- 
mate requires  ;  and,  in  some  cases,  bees-wax  may  be  substituted  in 
place  of  oil.  All  the  absorbent  and  solid  materials  must  be  kiln 
dried.  If  the  composition  is  not  to  be  any  other  color  than  white, 
the  lead  may  be  omitted,  by  taking  the  full  proportion  cf  the  other 
absorbents ;  and  also  white  or  red  lead  may  be  substituted  alone, 
instead  of  any  absorbent  material. 


STUCCO. 


01 


The  first  coat  of  this  composition  is  to  be  laid  on  with  a  trowel,  and 
floated  to  an  even  surface,  with  a  rule  or  handle  float.  The  second 
coat,  after  it  is  laid  on  with  a  trowel,  when  the  other  is  nearly  dry, 
should  be  worked  down  and  smoothed,  with  floats  edged  with  horn, 
or  any  hard,  smooth  substance,  that  does  not  stain.  It  may  be  prop- 
er, previously  to  laying  on  the  composition,  to  moisten  the  surface 
on  which  it  is  to  be  laid,  by  a  brush,  with  the  same  kind  of  oil  or  in- 
gredients, which  pass  through  the  levigating  machine,  reduced  to 
a  more  liquid  state,  in  order  to  make  the  composition  adhere  the 
better.  This  composition  admits  of  being  modelled,  or  cast  in 
moulds,  in  the  same  manner  as  plasterers,  or  statuaries  model  or  cast 
their  stucco-work.  It  also  admits  of  being  painted  upon,  and 
adorned  with  landscape,  or  ornamental,  or  figure  painting,  as  well 
as  plain  painting. 


CHAPTER  III. 


PRACTICAL  GEOMETRY,  ADAPTED  TO  MASONRY  AND 
STONE-CUTTING. 

SECTION  L 
ON  THE  POSITION  OF  LINES  AND  POINTS. 

As  the  construction  of  every  complex  object  in  nature  consists  of 
certain  combinations  of  the  simple  operations  of  geometry  ;  and  as 
positions  cannot  be  understood  without  angles  and  parallel  lines,  it 
will  be  necessary  to  treat  of  the  practical  part  of  this  science,  at 
least  as  far  as  the  operations  of  the  positions  of  lines  and  points  are 
concerned,  in  order  to  render  the  construction  and  the  language  of 
geometry  familiar  to  the  student  in  their  applications  to  the  prin- 
ciples of  Masonry. 

PROBLEM  I. 

From  a  given  point  in  a  given  straight  line  to  draw  a  perpen- 
dicular. 

Plate  1.  Let  AB,  Jig.  1.  be  a  given  straight  line,  and  c  the  given  point.  In 
AB  take  two  equal  distances,  cd  and  ce.  From  d  as  a  centre,  with  any  radius 
greater  than  cd  or  ce,  describe  an  arc  at  /,  and  with  the  same  radius,  from  the 
point  e,  describe  another  arc  intersecting  the  former  at  /,  and  draw  /c,  and  fc  is 
the  perpendicular  required. 

PROBLEM  II. 

From  the  one  extremity  of  a  straight  line  to  draw  a  perpendicular. 

Fig.  2.  Let  AB  be  the  given  straight  line,  and  let  it  be  required  to  draw  a 
perpendicular  from  the  extremity  B.  On  one  side  of  the  line  AB  take  any  con- 
venient point  c ;  and  from  c,  as  a  centre,  with  any  radius  that  will  cut  the  line, 
describe  an  arc  d  Be,  intersecting  AB  in  the  point  d;  through  c  draw  the 
diameter  de}  and  join  eB,  and  eB  is  the  perpendicular  required. 


ON  THE  POSITION  OF  LINES  AND  POINTS. 


63 


PROBLEM  III. 

From  a  given  point  out  of  a  straight  line  to  let  fall  a  per- 
pendicular. 

Fig.  3.  Let  AB  be  the  given  straight  line,  and  c  the  given  point ;  it  is  required 
to  draw  a  straight  line  from  c,  perpendicular  to  AB.  From  c,  as  a  centre, 
with  any  distance  that  will  cut  the  line  AB,  describe  an  arc  intersecting  AB  in 
the  points  d  and  e ;  from  rf,  as  a  centre,  with  any  radius  greater  than  the  half  of 
de,  describe  an  arc,  and  from  e,  with  the  same  radius,  describe  another  arc  inter- 
secting the  former  in  f,  and  draw/c,  and  fc  is  the  perpendicular  required. 

The  criterion  of  the  truth  of  the  method  of  Jig.  2,  is  that  of  the  angle  in  a 
semicircle  being  a  right  angle. 

PROBLEM  IV. 

At  a  given  point  in  a  given  straight  line,  to  make  an  angle  equal 
to  a  given  angle. 

Fig.  4.  Let  CBA  be  the  given  angle,  and  LF  the  given  straight  line.  Let  it 
be  required  to  draw  a  straight  line,  at  the  point  L,  to  make  an  angle  with  the 
line  LF,  equal  to  the  angle  CBA.  From  the  point  B,  with  any  radius,  describe 
an  arc  meeting  BA  in  h,  and  BC  in  g ;  and  from  the  point  L,  with  the  same  ra- 
dius, describe  an  arc  ik,  meeting  LF  in  i.  Make  ik  equal  to  gh,  and  through  k 
draw  the  straight  line  LD,  and  FLD  is  the  angle  required. 

PROBLEM  V. 

Through  a  given  point  /  to  draw  a  straight  line  parallel  to  a  given 
straight  line  AB. 

Fig.  5.  Let  /be  the  given  point,  and  AB  the  given  straight  line.  Draw  any 
straight  line  ft.  meeting  AB  in  e,  and  draw  gh,  making  the  angle  hgB  equal  to 
feB,  Make  gh  equal  to  ef.  Through  the  points  f  and  h  draw  the  line  CD,  and 
CD  is  parallel  to  AB,  as  required. 

PROBLEM  VI. 

To  draw  a  straight  line  parallel  to  a  given  straight  line  at  a  given 
distance  from  the  given  straight  line. 

Fig.  6.  Let  AB  be  the  given  straight  line  ;  it  is  required  to  draw  a  straight 
line  at  a  given  distance  from  BC.  In  AB  take  any  two  points  e  and  /;  from  e, 
with  the  given  distance,  describe  an  arc  gh ;  and  from  /,  with  the  same  distance, 
describe  another  arc  ik.  Draw  the  line  CD  to  touch  the  arcs  gh  and  ik,  and  CD 
is  parallel  to  AB,  as  required. 

PROBLEM  VII. 

To  bisect  a  given  straight  line  AB  by  a  perpendicular. 

Fig.  7.  From  the  point  A  as  a  centre,  with  any  radius  greater  than  the  half 
of  AB,  describe  an  arc  cd  ■  and  from  B,  with  the  same  radius,  describe  another 
arc  intersecting  the  former  at  c  and  d,  and  draw  cd,  intersecting  AB  in  e  ;  then 
AB  is  divided  in  c,  as  required. 

PROBLEM  VIII. 
Upon  a  given  straight  line  to  describe  an  equilateral  triangle. 
Fig,  8.   Let  AB  be  the  given  straight  line.    From  the  point  A,  with  the  ra- 


64 


OPERATIVE  MASONRY. 


dius  AB,  describe  an  arc,  and  from  the  point  B,  with  the  radius  BA,  describe 
another  arc,  intersecting  the  former  in  C,  and  draw  the  straight  lines  CA  and 
CB  ;  then  ABC  is  the  equilateral  triangle  required. 

PROBLEM  IX. 

Upon  a  given  straight  line  to  describe  a  triangle,  of  which  the 
sides  shall  be  equal  to  three  given  straight  lines,  provided  that  any 
one  of  the  three  given  lines  be  less  than  the  sum  of  the  other  two. 

Fig.  9.  Let  the  three  given  straight  lines  be  A,  B,  C,  and  let  DF  be  the 
straight  line  on  which  the  triangle  is  required  to  be  described.  Make  DF  equal 
to  the  given  straight  line  A.  From  D,  with  the  radius  of  the  line  B,  describe 
an  arc,  and  from  F,  with  the  radius  of  the  line  C,  describe  another  arc,  meet- 
ing the  arc  described  from  D  in  the  point  E.  Draw  ED  and  EF,  then  DEF  is 
the  triangle  required. 

PROBLEM  X. 

Given  the  base  and  height  of  the  segment  of  a  circle  to  find  the 
centre  of  the  circle,  and  thence  to  describe  the  arc. 

Fig.  10.  Let  AC  be  the  base,  bisect  AC  in  D  by  the  perpendicular  BE  ;  make 
DB  equal  to  the  height,  and  join  the  points  A  and  B.  Make  the  angle  BAE 
equal  to  ABE,  and  the  point  E  is  the  centre  required. 

From  the  point  E,  with  the  radius  EA  or  EB,  describe  the  arc  ABC  ;  then 
ABC  is  the  arc  required. 

N.  B.  The  centre  must  also  have  been  found  by  bisecting  AB  by  a  perpendicu- 
lar, which  would  have  met  BE  in  the  point  E. 

PROBLEM  XI. 

Given  two  converging  lines,  through  a  given  point  in  one  of  them, 
to  draw  a  third  straight  line,  so  that  the  angles  on  the  same  side  of 
the  line  thus  drawn,  made  by  this  line  and  each  of  the  first  two 
given  lines,  may  be  equal  to  each  other. 

Fig.  11.  Let  the  two  converging  lines  be  AC  and  BD,  and  let  A  be  the  giv- 
en point.  Draw  AE  parallel  to  BD  ;  bisect  the  angle  CAE  by  the  straight  line 
AB  ;  then  will  the  angles  CAB  and  DBA  be  equal  to  one  another. 

For,  suppose  AE  to  be  produced  from  A  to  F,  and  suppose  AC  and  BD  to  be 
produced  to  meet  in  some  point  G,  then  AC  would  have  been  a  line  falling  upon 
the  two  parallel  straight  lines  AF  and  BD,  and  consequently  making  the  angle 
at  G  equal  to  the  angle  FAC  ;  and  since  the  three  angles  of  every  triangle  are 
equal  to  two  right  angles,  and  since  the  angles  FAC,  CAB,  BAE,  are  also  equal 
to  two  right  angles,  and  since  FAC  is  equal  to  the  vertical  angle  of  the  triangle, 
the  angle  CAE  is  equal  to  the  sum  of  the  angles  at  the  base ;  and  therefore, 
since  CAB  is  half  the  sum,  the  angle  ABD  must  be  equal  to  the  other  half. 

PROBLEM  XII. 

Given  two  converging  lines,  to  describe  the  arc  of  a  circle  through 
a  given  point  in  one  of  them,  without  having  recourse  to  a  centre, 
so  that  the  point  of  convergency  may  be  in  the  centre  of  the  arc. 

Fig.  12.  Let  AB  and  EF  be  the  two  converging  lines,  and  A  the  given  point 
through  which  the  arc  is  to  pass.    Draw  AE,  making  the  angles  BAE  and  FE  A 


OF  CURVED  LINES. 


65 


equal  to  each  other.  Bisect  AE  by  the  perpendicular  CD,  and  draw  Ah,  making 
the  angles  BAh  and  D/iA  equal  to  one  another ;  then  Ah  is  the  chord  of  the 
arc,  and  nh  is  the  versed  sine.  Suppose  now  that  the  three  points  A,  h,  E,  are 
transferred  to  A,  B,  C,  fig.  13.  Join  BA  and  BC.  Produce  BA  to  d,  and  BC  to 
e.  Make  the  edge  of  a  slip  of  wood  to  the  angle  dBe.  Move  the  edge  dBe  of 
the  slip  of  wood  so  that  the  point  B  may  be  upon  A  ;  then  move  this  slip  again, 
so  that  while  the  part  Bd  of  the  edge  of  the  slip  is  sliding  upon  the  pin  at  A, 
and  the  part  Be  upon  the  pin  at  C,  a  pencil  held  to  the  angle  B,  will  describe  a 
curve  ;  then  this  curve  will  be  the  arc  required. 

PROBLEM  XIII. 

Given  two  straight  lines  to  find  a  third  porportional. 

Fig.  14.  From  any  point  A,  draw  any  two  straight  lines  BA,  AC,  at  any  an- 
gle. Make  AB,  equal  to  one  of  the  given  straight  lines,  and  AC  equal  to  the 
other ;  and  in  AB  make  Ad  equal  to  AC.  Join  BC  and  draw  de  parallel  to  BC, 
meeting  AC  in  c  ;  then  Ac  is  the  third  proportional  required. 

Or  if  Ae  be  equal  to  one  of  the  given  straight  lines,  and  Ad  equal  to  the  oth- 
er. Make  AC  equal  to  Ad.  Join  de  and  draw  CB  parallel  to  ed,  then  AB  is  the 
third  proportional. 

PROBLEM  XIV. 

Given  a  straight  line,  and  how  divided,  to  divide  another  in  the 
same  proportion. 

Fig.  15.  Draw  the  lines  BA,  AC  as  in  the  preceding  problem,  and  let  AB 
be  the  given  divided  line,  d  and  e  being  the  points  of  division,  and  let  AC  be  the 
line  to  be  divided.  Join  BC  and  draw  eg  and  df  parallel  to  BC,  meeting  AC  in 
f  and  g ;  then  AC  is  divided  in / and  g,  in  the  same  proportion  as  AB  is  divided 
in  the  points  d  and  e. 

PROBLEM  XV. 

Given  three  straight  lines  to  find  a  fourth  proportional. 

Fig.  15.  The  angle  BAC  being  made  as  before ;  let  Ae  be  equal  to  one  of  the 
given  lines,  Ad  equal  to  a  second,  and  af  equal  to  the  third.  Join  df  and  draw 
eg  parallel  to  df;  then  Ag  is  the  fourth  proportional. 

SECTION  II. 

ON  THE  SPECIES,  NATURE,  AND  CONSTRUCTION  OF  CURVE 

LINfiS. 

The  geometrial  orders  of  lines  employed  in  architecture  in  the 
construction  of  arches,  are  circular  and  elliptic,  and  occasionally 
parabolic,  hyperbolic,  cycloidal,  and  catenarian  curves. 

In  houses,  the  chief  lines  employed  in  the  construction  of  arches 
and  vaults,  are  circular  and  elliptic  curves,  generally  a  semi,  and 
sometimes  less,  but  seldom  or  never  greater.  When  a  circular  or 
elliptic  arc  is  adopted,  one  of  the  axes  of  the  curve  is  most  frequently 


C6 


OPERATIVE  MASONRY. 


situated  upon  the  springing  line  ;  but  is  sometimes  placed  so  as  to 
be  parallel  to  it.  The  most  usual  portions  of  circular  or  elliptic 
curves  are  the  semi  ;  and  in  the  pointed  style  of  architecture,  para- 
bolic and  hyperbolic  curves  are  very  frequently  employed. 

In  bridge  building,  besides  circular  and  elliptic  curves  which  are 
the  most  often  used  in  the  construction  of  stone  arches,  cycloidal 
curves  may  also  be  introduced.  In  chain  bridges,  or  bridges  of  sus- 
pension, not  only  the  circular  and  parabolic  curves,  but  that  of  the 
catenarian  may  be  employed.  The  suspending  chains  necessarily 
assume  the  form  of  catenarian  curves  ;  but  the  road-way  may  be 
any  curve  line  whatever  ;  but  as  all  curves  are  nearly  circular  at 
the  vertex,  it  will  be  better  to  employ  those  in  the  construction  of 
works  which  are  susceptible  of  the  most  easy  calculation. 

Among  the  numerous  orders  of  curve  lines,  the  parabolic  affords 
the  most  easy  means  of  computing  its  ordinates  and  tangents,  which 
will  be  found  necessary  in  ascertaining  the  rke  and  inclination  of 
the  road-way  in  all  points  of  the  curve,  from  either  extreme  to  the 
centre  of  the  bridge. 

The  base  of  an  arc  is  that  upon  which  the  arc  is  supposed  to 
stand  ;  and  the  highest  point  of  an  arc  is  that  in  which  a  straight 
line  parallel  to  the  base  would  meet  the  curve,  without  the  possibility 
of  coming  within  the  area  included  by  the  curve  and  its  base,  and 
this  point  is  called  the  summit  of  the  arc. 

As  the  curves  employed  in  building  are  generally  symmetrical, 
therefore  they  are  equal  and  similar  on  each  side  of  the  summit,  and 
their  areas  are  equal  and  similar  on  each  side  of  the  perpendicular 
from  the  middle  of  the  base. 

PROBLEM  I. 
To  describe  a  semi-ellipse  upon  the  transverse  axis. 

Plate  II.  Let  Aa,  Jig.  1,  be  the  axis  major,  and  let  BC  bisecting  Act  perpen- 
dicularly in  the  point  C,  be  the  semi-conjugate  axis. 

Upon  the  straight  edge  mi  of  a  rule,  mark  the  point  m  at  or  near  one  of  its 
ends,  and  the  point  I  at  a  distance  ;  from  m  equal  to  BC,  the  semi-conjugate  axis  ; 
and  the  point  k  at  a  distance  from  m,  equal  to  AC  or  Ca  the  semi-transverse 
axis  ;  the  distance  kl  being  equal  to  the  difference  of  the  two  axes.  To  find  any 
point  in  the  curve,  place  the  point  k  in  the  line  BC  produced,  and  the  point  I  in 
the  axis  Aa  ;  and  mark  the  paper  or  plane  on  which  the  figure  is  to  be  described 
at  the  point  m.  Proceed  in  this  manner  until  a  sufficient  number  of  points  are 
found,  and  draw  a  curve  through  them,  and  the  curve  will  be  the  semi-ellipse 
required. 

PROBLEM  II. 

Upon  a  given  double  ordinate  to  describe  the  segment  of  an  el- 
lipse, to  a  given  abscissa,  and  to  a  given  semi-axis  in  that  abscissa. 

Fig.  2  and  3.  Let  Mm  be  the  double  ordinate,  PH  the  abscissa,  and  HC 
the  semi-axis. 

Through  the  centre  C,  draw  Kk  parallel  to  Mm.  From  either  extremity  m  of  the 
double  ordinate  as  a  centre  with  the  distance  HC  of  the  given  semi-axis,  as  radius 
describe  an  arc  intersecting  Kk  in  r.    Draw  mr  intersecting  HC  in  q,  or  produce 


OF  CURVE  LINES. 


67 


mr  and  HC  to  meet  in  q ;  then  mq,  fig.  2,  will  be  the  semi-transverse,  and  mr 
the  semi-conjugate,  and  in  fig.  3  the  contrary  will  take  place,  mr  will  be  the  semi- 
transverse,  and  mq  the  semi-conjugate ;  the  two  axes  being  thus  found,  the  curve 
may  be  described  as  in  the  immediately  preceding  problem. 

PROBLEM  nr. 

Given  two  conjugate  diameters  to  find  any  number  of  points  in 
the  curve,  and  thence  to  describe  it. 

Figs.  4  and  5.  Let  Aa,  Bb,  be  the  conjugate  diameters.  Draw  AD  parallel  to 
BC,  and  BD  parallel  to  CA.  Divide  AD  and  AC  each  into  the  same  number  of 
equal  parts.  Through  the  points  of  division  in  AC  draw  straight  lines  from  b, 
and  through  the  points  of  division  in  AD  draw  other  straight  lines  to  the  point 
B,  meeting  those  drawn  from  b  in  the  points  f,  g,  h.  Draw  a  curve  line  through 
the  points  A,f,g,  h,  B,  which  will  be  one  quarter  of  the  whole  figure.  The  other 
three  will  of  course  be  found  in  the  same  manner. 

PROBLEM  IV. 

To  draw  a  normal,  or  line  perpendicular  to  the  curve  of  an  ellipse 
at  a  given  point  in  the  curve. 

Fig.  6.  Let  the  curve  be  ABa,  and  let  Aa  be  the  transverse  axis,  and  CB  the 
semi-conjugate,  and  let  it  be  required  to  draw  a  line  from  the  point  n- perpen- 
dicular to  the  curve.  With  AC  the  semi-axis  major  as  a  radius ;  from  the  point 
B  describe  an  arc,  intersecting  Aa  in  the  foci,  f,f.  From  the  points  f,f,  and 
through  the  point  n,  draw/'  d  and  /e,and  bisect  the  angle  end,  and  the  bissecting 
line  nN  will  be  perpendicular  to  the  curve  as  required. 

PROBLEM  V. 

To  draw  a  tangent  to  the  curve  of  an  ellipse  at  a  given  point. 

Fig.  6.  Let  to  be  the  given  point.  Draw  fm,  and  produce/m.  to  g,  and  join 
the  points/,  m.  Bisect  the  angle/  mg,  and  the  bisecting  line  Tt  will  be  the  tan- 
gent required. 

PROBLEM  VI. 

The  curve  of  an  ellipse  being  given,  to  find  the  two  axes. 

Fig.  7.  Let  AMNnwi  be  the  given  curve  within  the  figure  ;  draw  any  two  par- 
allel lines  Mto,  Nn.  Bisect  Mm  in  o,  and  Nn  in  p,  and  draw  the  straight  line  Aopa. 
Bisect  Aa  in  C,  from  C  as  a  centre,  with  any  radius  that  will  cut  the  curve  ;  de- 
scribe the  arc  rr',  intersecting  the  curve  in  the  points  tV,  and  draw  the  straight 
line  rr1.  Bisect  mr1  in  h,  and  through  the  points  h  and  C  draw  the  line  de,  then 
de  is  the  axis  major ;  and  a  line  drawn  through  the  point  C  at  right  angles  to  def 
to  meet  the  curve  on  each  side  of  C  will  be  the  axis  minor. 

PROBLEM  VII. 

With  a  given  abscissa  and  ordinate,  to  describe  a  parabola. 

Fig.  8.  Let  AB  be  the  abscissa,  and  BC  the  ordinate.  Draw  CD  parallel  to 
BA,  and  AD  parallel  to  BC.  Divide  CD  and  CB  each  into  the  same  number  of 
equal  parts.  From  the  points  1,  2,  3  in  CD  draw  lines  to  A,  and  from  the  points 
L  2,  3  in  CB,  draw  lines  parallel  to  BA,  meeting  the  former  lines  to  A  in  the 


68 


OPERATITE  MASONRY. 


points  /,  g,  h.  Draw  the  curve  CfghA,  which  will  be  one  half  of  the  parabola, 
the  other  half  will  be  found  in  the  same  manner.  The  radius  of  curvature  at  the 
point  A,  is  half  the  parameter. 

PROBLEM  VIII. 
The  curve  of  a  parabola  being  given,  to  find  the  parameter. 

Fig.  8.  Let  CAN  be  the  curve  of  the  parabola.  Bisect  BC  in  the  point  2, 
and  draw  A2  and  2d  perpendicular  to  A2,  meeting  AB  produced  in  d ;  then  Bd 
is  one  fourth  part  of  the  parameter. 

For  AB  :  B2  : :  B2  :  Bd,  now  let  AB=a,  BC=6,  then  B2=£6,  hence  a  : 

62 

kb  "  I  k°  :  hp  5  whence  ap=b2  or  p= — . 

a 

PROBLEM  IX. 

To  draw  a  tangent  to  any  point  M,  in  the  curve  of  a  parabola. 

Fig.  8.    Draw  the  ordinate  PM,  and  produce  PA  to  q.    Make  A  q  equal  to 
AP,  and  draw  the  straight  line  q  M  ;  then  q  M  will  be  the  tangent  required. 
For  the  subtangent  of  the  curve  is  double  to  the  abscissa. 

PROBLEM  X. 
To  form  the  curve  of  a  parabola  by  means  of  tangents. 

Fig.  9.  Let  AC  be  the  double  ordinate.  Draw  DB  bisecting  AC,  and  make 
DB  equal  to  the  abscissa.  Produce  DB  to  E,  and  make  BE  equal  to  BD.  Draw 
the  two  straight  lines  EA  and  EC.  Divide  AE  and  EC  each  in  the  same  pro- 
portion, or  into  the  same  number  of  equal  parts  at  the  points  1,  2,  3,  &c.  in  each 
line.  Draw  the  straight  lines  1-1,  2-2,  3-3,  &c.  and  their  intersections  will  cir- 
cumscribe the  curve  of  the  parabola  as  required. 

Scholium.  Small  portions  of  the  curves  of  conic  sections,  near  to  the  vertices, 
may  be  described  with  compasses  so  as  not  to  be  perceptible  ;  and  thus,  not  only 
in  the  parabola,  but  in  the  ellipse  ;  and  in  the  hyperbola,  the  radius  of  Curvature 
at  the  vertices  is  half  the  parameter,  which  passes  through  the  focus.  In  the 
parabola,  the  parameter  is  a  third  proportional  to  the  abscissa  and  ordinate  ;  and 
in  the  ellipse,  and  hyperbola,  the  parameter  is  a  third  proportional  to  the  transverse 
and  conjugate  axis ;  and  therefore  may  be  easily  found  by  lines  or  by  calculation 
on  large  works,  such  as  bridges,  &c. 


&  U¥T EMJE C TI QN  OF  FJLAI^ES  « 


Tlate  3 . 


OF  LINES  AND  PLANES,  &c. 


69 


SECTION  III. 

OF  THE  POSITION  OF  LINES  AND  PLANES,  AND  THE  PROP- 
ERTIES ARISING  FROM  THEIR  INTERSECTIONS. 

A  plane  is  a  surface  in  which  a  straight  line  may  coincide  in  all 
directions. 

A  straight  line  is  in  a  plane,  when  it  has  two  points  in  common 
with  that  plane. 

Two  straight  lines  which  cut  each  other  in  space,  or  would  inter- 
sect, if  produced,  are  in  the  same  plane  ;  and  two  lines  that  are 
parallel,  are  also  in  the  same  plane. 

Three  points  given  in  space,  and  not  in  a  straight,  are  necessary 
and  sufficient  for  determining  the  position  of  a  plane.  Hence  two 
planes  which  have  three  points  common,  coincide  with  each  other. 

The  intersection  of  two  planes  is  a  straight  line. 

Plate  III.  When  two  planes  ABCD,  ABFE,  Jig.  1,  intersect,  they  form  be- 
tween them  a  certain  angle,  which  is  called  the  inclination  of  the  two  planes, 
and  which  is  measured  by  the  angle  contained  by  two  lines  ;  one  drawn  in  each 
of  the  planes  perpendicular  to  their  line  of  common  section. 

Thus,  if  the  line  AF,  in  the  plane  ABEF,  be  perpendicular  to  AB,  and  the  line 
AD,  in  the  plane  ABCD,  be  perpendicular  also  to  AB,  then  the  angle  FAD  is 
the  measure  of  the  inclination  of  the  planes  ABEF,  ABCD.  When  the  angle 
FAD  is  a  right  angle,  the  two  planes  are  perpendicular. 

Fig.  2.  A  line  AB,  is  perpendicular  to  a  plane  PQ,  when  the  line  AB  is  per- 
pendicular to  any  line  BC  in  the  plane  PQ,,  which  passes  through  the  point  B, 
where  the  line  meets  the  plane.  The  point  B  is  called  the  foot  of  the  perpen- 
dicular. 

A  line  AB,  Jig.  3,  is  parallel  to  a  plane  PQ,  when  the  line  AB  is  parallel  to 
another  straight  line  CD,  in  the  plane  PQ. 

If  a  straight  line  have  one  of  its  intermediate  points  in  common  with  a  plane, 
the  whole  line  will  be  in  the  plane. 

Two  planes  are  parallel  to  one  another  when  they  cannot  intersect  in  any 
direction. 

The  intersections  of  two  parallel  planes  with  a  third  are  parallel.  Thus  in  Jig. 
4,  the  lines  AB,  CD,  comprehended  by  the  parallel  plane  PQ,  RS,  are  parallel. 

Any  number  of  parallel  lines  comprised  between  two  parallel  planes,  are  all 
equal.  Thus  the  parallel  lines  Act,  B6,  Cc,  .  .  .  .  ,  comprised  by  the  parallel 
planes  PQ,  RS,  are  all  equal. 

If  two  planes  CDEF,  GHIJ,  Jig.  6,  are  perpendicular  to  a  third  plane  PQ, 
their  intersection  AB  will  be  perpendicular  to  the  third  plane  PQ. 

If  two  straight  lines  be  cut  by  several  parallel  planes,  these  straight  lines  will 
be  divided  in  the  same  proportion. 


70 


OPERATIVE  MASONRY. 


SECTION  IV. 
OF  THE  RIGHT  SECTIONS  OF  ARCHES  OR  VAULTS. 
PROBLEM  I. 

To  describe  the  arc  of  a  circle  which  shall  have  a  given  tangent 
at  a  given  point,  and  which  shall  touch  another  given  arc. 

Plate  IV.  Let  Bk,  Jig.  1,  be  one  of  the  given  arcs,  and  lau  the  other,  and  let 
it  be  required  to  describe  the  arc  of  a  circle,  which  shall  touch  the  arc  Bk,  in 
the  point  k,  and  the  arc  lau  in  some  point  to  be  found  ;  let  g  be  the  centre  of  the 
arc  Bk. 

Draw  gk,  and  make  kp  equal  to  the  radius  of  the  circle  lau.  Draw  a  straight 
line  from  p  to  q,  the  centre  of  the  arc  lau,  and  bisect  pq,  by  a  perpendicular, 
meeting  kg  in  m.  Join  the  points  m,  q,  and  prolong  mq  to  Z.  It  is  manifest  that 
mk  and  ml  are  equal ;  therefore,  from  m  with  the  radius  mk  or  ml  describe  an  arc 
kl;  and  kl  will  be  the  arc  required. 

PROBLEM  II. 

To  describe  an  oval,  representing  an  ellipse,  to  any  given  dimen- 
sions of  length  and  breadth,  given  in  position. 

Let  Aa,  Bb,fig.  2,  be  the  two  given  lines  bisecting  each  other  in  C ;  Aa  being 
equal  to  the  length,  and  Bb  to  the  breadth. 

Find  a  third  proportional  to  this  semi-axis  Ca,  CB,*  and  make  ah  equal  to  the 
third  proportional ;  also  find  a  third  proportional  to  CB,  Caf  and  make  Bg 
equal  to  the  third  proportional. 

Make  the  angle  Bgk  equal  to  about  15°,  and  let  gk  meet  Aa  in  the  point  i. 
From  g  with  the  radius  gB,  describe  an  arc  Bk,  and  from  h  with  the  radius  ha, 
describe  an  arc  la.  Describe  the  arc  kl  by  the  preceding  problem  to  touch  the 
arc  Bk  in  k,  and  to  touch  the  arc  al  at  I,  and  thus  one  quarter  of  the  oval  will 
be  completed  ;  the  other  three  will  be  found  by  placing  the  centres  in  their  prop- 
er positions. 

Three  or  more  points  a,  b,  c,  might  easily  have  been  found  in  the  curve.  Thus, 
draw  Ad  parallel  to  Bb,  and  Bd  parallel  to  CA.  Divide  Ad  into  four  equal  parts, 
and  divide  AC  also  into  four  equal  parts  at  1,  2,  3.  From  b  and  through  1,  2,  3 
in  CA,  draw  ba,  bb,  be,  and  from  the  points  1,  2,  3  in  Ad,  draw  towards  B,  to  in- 
tersect the  former  in  a,  b,  c,  so  that  we  may  find  the  radius  of  curvature  upon  the 
sides,  and  at  the  two  ends,  by  finding  the  centre  of  a  circle  passing  through  three 
points  at  each  extremity,  the  extremity  being  the  middle  point. 


*  Thus  in  fig.  3,  draw  the  two  lines  G  A,  AH  making  an  angle  with  each  other  ;  make  ac 
equal  to  aC,  fig.  2,  and  Ad  equal  to  CB,  fig.  2,  and  make  Ae  equal  to  Ad.  Join  cd,  and 
draw  ef  parallel  to  cd  J  then  af  is  the  third  porportional. 

t  That  is,  in  fig.  3,  make  Ac  equal  AG  or  aC,  fig.  2,  and  Ac?  equal  to  CB  or  Cb,fig.  2,  and 
make  AG  equal  to  Ac  and  join  cd.  Draw  GH  parallel  to  dc  J  then  AH  is  the  third  pro- 
portional. 


TL  4. 


ON  THE  RIGHT  SECTIONS  OF  ARCHES. 


71 


Fig.  4  exhibits  the  use  of  this  method  of  describing  an  oval,  in  finding  the  di- 
rection of  the  joints  of  arches  so  as  to  agree  with  the  normals  drawn  from  the 
several  divisions  of  the  inner  arc.    The  arcs  are  marked  the  same  as  in  figure  2. 

REMARK. 

When  the  height  of  the  arch  is  equal  to,  or  greater  than  half  the  span,  and 
when  it  is  not  necessary  that  the  vertical  angle  should  be  given,  the  curves  of 
the  intrados  and  extrados  on  the  one  side  may  be  described  from  the  same  cen 
tre,  as  also  those  of  the  other  side  from  another  centre. 

The  most  easy  Gothic  arch  to  describe,  is  that  of  which  the  height  of  the  in- 
trados is  such  as  to  be  the  perpendicular  of  an  equilateral  triangle,  described 
upon  the  sparing  line  as  abase,  and  these  centres  are  the  points  to  which  the  ra- 
diating joints  must  tend. 

Gothic  arches  seldom  exceed  in  height  the  perpendicular  of  the  equilateral 
triangle  inscribed  in  the  intrados  of  the  aperture  ;  but  when  the  arch  is  sur- 
mounted, and  the  height  less  than  the  perpendicular  of  the  equilateral  triangle 
made  upon  the  base,  draw  a  straight  line  from  one  extremity  of  the  base  to  the 
vertex,  and  bisect  this  line  by  a  perpendicular.  From  the  point  where  the  per- 
pendicular meets  the  base  of  the  arch,  and  with  a  radius  equal  to  the  distance 
between  this  point  and  the  extremity  of  the  base  joined  to  the  vertex,  describe 
an  arc  between  the  two  points,  joined  by  the  straight  line,  and  the  curve  which 
forms  one  side  of  the  intrados  will  be  complete.  In  the  same  manner  will  be 
found  the  curve  on  the  other  side,  see  Jig.  5,  so  that  by  only  two  centres  the 
whole  of  the  intrados  will  be  formed. 

The  curves  of  all  kinds  of  Gothic  arches  whatever,  may  be  described  by  means 
of  conic  parabola,  to  a  given  vertical  angle,  and  to  any  given  dimensions.  Thus 
in  Jig.  6,  let  Ce,  Cf,  be  the  two  tangents,  and  Ae,  and  B/,  the  heights  of  their  ex- 
tremities. Divide  Ae  and  eC  each  into  the  same  number  of  equal  parts  by  the 
points  1,  2,  3,  in  each  of  these  lines.  Draw  lines  from  the  corresponding  points 
1-1,  2-2,  3-3,  &c. ;  and  the  intersections  will  form  the  curve  of  one  side  of  the  in- 
trados, as  we  have  already  seen.  The  curve  on  the  other  side  will  be  formed  in 
the  same  manner. 

Join  BC,  and  bisect  it  in  g  and  join  gt,  intersecting  the  curve  in  I.  Draw  hk 
parallel  to  CB,  meeting  gf  in  k.  Make  li  equal  to  Ik,  and  ih  joined  is  a  tangent 
at  h.    Hence,  hm  perpendicular  to  hi,  is  the  joint. 


10 


CHAPTER  IV. 


SECTION  I. 

ON  THE  NATURE  AND  CONSTRUCTION  OF  TREHEDRALS. 

DEFINITIONS. 

Every  stone  bounded  by  six  quadrilateral  planes  or  faces  forms  a 
solid,  of  which  the  surfaces  terminate  on  eight  points,  every  three 
surfaces  in  one  point.  Every  three  planes  thus  terminating  is  term- 
ed a  solid  angle  or  trehedral. 

The  angles  formed  by  the  intersections  of  the  faces  with  one 
another,  or  the  three  plain  angles,  are  called  sides  of  the  trehedral, 
and  the  angles  of  inclination  are  called,  by  way  of  distinction  from 
the  other,  simply  angles. 

The  three  sides,  as  well  as  the  three  angles,  are  each  called  apart; 
so  that  the  whole  trehedral  consists  of  six  parts  ;  and  if  any  three 
of  these  parts  be  given,  the  remaining  three  can  be  found. 

Therefore,  in  bodies  constructed  of  stone,  which  are  intended  to 
have  their  solid  angles  to  consist  of  three  plane  angles,  the  con- 
struction of  such  bodies  may  be  reduced  to  the  consideration  of  the 
trehedral. 

As  to  the  remaining  surface  of  the  solid  which  incloses  the  solid, 
completely  making  a  fourth  side  to  the  trehedral,  it  may  be  of  any 
form  whatever,  regular  or  irregular,  or  consisting  of  many  surfaces  : 
it  or  they  have  nothing  to  do  in  the  construction. 

The  parts  of  the  trehedral,  which  may  be  obtained  from  three 
given  parts,  are  the  very  same  as  three  parts  found  in  a  spherical 
triangle  from  three  given  parts.  This  is,  in  fact,  the  same  as  spher- 
ical trigonometry. 

We  shall  not,  however,  enter  into  any  operose  analytical  investi- 
gations, but  treat  the  subject  in  the  most  simple  manner,  according 
to  the  rules  of  solid  geometry  ;  and  only  those  trehedrals,  which 
have  two  of  their  planes  at  a  right  angle  with  each  other,  (though 
there  are  many  cases  in  which  the  oblique  trehedral  would  be  neces- 
sary) ;  as  the  bounds  prescribed  for  this  work  will  not  admit  of  such 
an  extension  of  the  principles. 


'Plate  S. 


* 


\ 


ON  TREIIEDRALS. 


73 


If  the  trehedral  have  two  of  its  planes  perpendicular  to  each  other, 
it  is  called  a  right  angled  trehedral ;  each  of  the  two  faces  thus  form- 
ing a  right  angle,  is  called  a  legy  and  the  remaining  side  joining  each 
leg,  is  called  the  hypothenuse. 

PROBLEM  I. 

Given  two  legs  of  a  right  angled  trehedral,  to  find  the  hypothenuse. 

Plate  V.  figs.  1,  2,  3,  4.  Let  PON  and  POR  be  the  given  legs.  Draw  PR 
perpendicular  to  OP,  and  PQ  perpendicular  to  ON.  From  O,  as  a  centre  with 
the  radius  OR,  describe  an  arc  intersecting  PQin  Q,  and  join  OQ,  and  QON  is 
the  hypothenuse  required. 

Demonstration. — Suppose  the  triangle  POR  revolved  upon  OP,  until  PR  be- 
come perpendicular  to  the  plane  of  the  triangle  OPN,  then  the  plane  of  the  tri- 
angle OPR  will  be  perpendicular  to  the  plane  of  the  triangle  OPN. 

Again,  suppose  the  triangle  ONQ  to  revolve  upon  ON,  and  let  PQ,  or  PQ, 
produced  intersect  ON  in  m,  then  mQ  will  always  be  in  a  plane  passing  through 
Pm  and  the  plane  described  by  mQ  will  be  perpendicular  to  the  plane  mOP  ; 
and  as  PR  is,  by  supposition,  also  perpendicular  to  the  plane  mOP,  therefore  PR 
and  mQ  being  thus  situated  in  the  same  plane  will  meet,  except  they  are  parallel. 

Let  mQ  therefore  be  revolved  until  the  straight  line  mQ  fall  upon  the  point  R  J 
let  Q  then  be  supposed  to  coincide  with  R;  then  because  Q,  by  supposition,  coin- 
cides with  R,  and  the  point  O  is  common  to  the  straight  lines  OQ  and  OR,  there- 
fore the  straight  lines  OQ  and  OR  having  two  common  points  will  coincide,  and 
therefore  mOQ  will  be  the  hypothenuse  required. 

PROBLEM  II. 

Given  the  hypothenuse,  and  one  of  the  legs,  to  find  the  other  leg. 

Figs.  1,  2.  3,  4.  Let  NOQ  be  the  given  hypothenuse  and  NOP  the  given  leg, 
and  let  these  two  parts  be  attached  to  each  other  by  the  straight  line  ON. 

In  ON  take  any  point  m,  and  through  m  draw  PQ  perpendicular  to  ON. 
Draw  PR  perpendicular  to  OP.  From  the  point  O,  with  the  radius  OQ,  de- 
scribe an  arc  QR  and  join  OR ;  then  will  POR  be  the  other  leg,  as  required. 

These  four  diagrams  show  the  various  positions  in  which  the  data  may  be 
placed  :  every  one  will  frequently  occur  in  practice. 

PROBLEM  III. 

Given  the  two  legs  of  a  right-angled  trehedral,  to  find  one  of  the 
angles  at  the  hypothenuse. 

Figs.  5,  6.  Let  the  two  given  legs  be  PON  and  POR.  In  OP  take  any  point 
P,  and  draw  PN  perpendicular  to  ON,  and  PR  perpendicular  to  PO,  and  PK  par- 
allel to  ON.  Make  PK  equal  to  PR,  and  join  NK  ;  then  PNK  will  be  the  angle 
at  the  hypothenuse. 

In  fig.  5,  the  two  legs  lie  upon  separate  parts;  and  in  fig.  G,  one  of  the  legs  lies 
upon  the  other. 

Fig.  7,  exhibits  the  same  principle  applied  in  finding  a  series  of  bevels  or 
angles  made  by  the  hypothenuse  and  a  leg.  Thus  let  the  two  legs  be  PON  and 
POR  From  any  point  m  in  OP  draw  mR  perpendicular  to  OP.  On  Om,  as  a 
diameter,  describe  the  semicircle  Oqm,  intersecting  ON  in  q,  and  join  qm.  Make 
mr  equal  to  mq,  and  join  rR ;  then  Pr  R  will  be  the  angle  required. 


74 


OPERATIVE  MASONRY. 


PROBLEM  IV. 

Given  one  of  the  legs  and  the  inclination  of  the  hypothenuse  to 
that  leg,  to  find  the  other  leg. 

Figs.  8,  and  9.  Let  NOP  be  the  given  leg.  In  ON  take  any  point  m,  and 
draw  mi  perpendicular  to  ON.  Make  imp  equal  to  the  angle  which  the  leg  NOP 
makes  with  the  hypothenuse.  Through  any  point  i,  in  mi,  draw  Pp  parallel  to 
ON,  and  PQ,  perpendicular  to  OP.  Make  PQ  equal  to  ip,  and  join  OQ,  and 
QOP  will  be  the  other  leg. 

PROBLEM  V. 

Given  one  of  the  legs  and  the  angle  which  the  hypothenuse  forms 
with  that  leg  to  find  the  hypothenuse. 

Figs.  10,  and  11.  In  NO,  take  any  point  m,  and  draw  mn  perpendicular  to 
ON.  Make  nmp  equal  to  the  angle  which  the  hypothenuse  makes  with  the  leg 
NOP.  From  the  point  m  as  a  centre  with  any  radius,  mn  describe  an  arc  np. 
Draw  pP,  nQ  parallel  to  NO,  and  PQ  perpendicular  to  NO,  and  join  OQ, ;  then 
NOQ  is  the  hypothenuse  required. 

GENERAL  APPLICATIONS  OF  THE  TREHEDRAL  TO  TANGENT  PLANES. 

EXAMPLE  I. 

Given  the  inclination  and  seat  of  the  axis  of  an  oblique  cylinder 
or  cylindroid,  to  find  the  angle  which  a  tangent  makes  at  any  point 
in  the  circumference  of  the  base,  with  the  plane  of  the  base. 

Figs.  1,  3,  Plate  VI.  Let  AEBO  be  the  base  of  the  cylinder  or  cylindroid, 
CB  the  seat  of  the  axis,  and  let  BCD  be  the  angle  of  inclination,  and  let  O  be  the 
point  where  the  tangent  plane  touches  the  curved  surface  of  the  solid. 

Draw  ON  a  tangent  line  at  the  point  O  in  the  base,  and  draw  OP  parallel  to 
CB.    Make  the  angle  POR  equal  to  BCD,  and  draw  PR  perpendicular  to  PO. 

Then,  if  the  triangle  POR  be  conceived  to  be  revolved  round  the  line  PO  as 
an  axis,  until  its  plane  become  perpendicular  to  the  plane  of  the  circle  AEBC,  the 
straight  line  OR  will,  in  this  position,  coincide  with  the  cylindrical  surface,  and 
a  plane  touching  the  cylinder  or  cylindroid  at  O,  will  pass  through  the  lines  ON 
and  OR.  Here  will  now  be  given  the  two  legs  POR  and  PON  of  a  right  angled 
trehedral  to  find  the  angle  which  the  hypothenuse  makes  with  the  base.  Draw 
PQ  perpendicular  to  ON,  intersecting  it  in  m,  and  draw  PS  perpendicular  to  PQ. 
Make  PS  equal  to  PR,  and  join  mS  ;  then  PmS  is  the  angle  required. 

The  hypothenuse  will  be  easily  constructed  at  the  same  time,  thus — make  mQ, 
equal  to  mS,  and  join  OQ,  then  NOQ  will  be  the  hypothenuse  required. 

In  Jig.  1,  the  method  of  finding  the  angle  which  the  tangent  plane  makes  with 
the  base  and  the  hypothenuse  is  exhibited  at  four  different  points.  In  the  two 
first  points  O  from  A  in  the  first  quadrant,  the  tangent  planes  make  an  acute  angle 
at  each  point  O ;  but  in  the  second  quadrant,  they  make  an  obtuse  angle  at  each 
point  O. 

Fig.  2  is  the  second  position  of  the  construction  from  the  point  A,  for  finding 
the  angle  which  the  tangent  plane  makes  with  the  base,  and  for  finding  the  hypo- 
thenuse enlarged;  in  order  to  show  a  more  convenient  method  by  not  only  requir- 
ing less  space,  but  less  labor.  It  may  be  thus  described,  the  two  given  legs  being 
FO  R  and  P  O  N'. 


9lale  6. 


ON  THE  PROJECTION  OF  A  STRAIGHT  LINE,  &,c.  75 


Draw  P'm'  perpendicular  to  O'N',  meeting  ON  in  m'.  In  P  O',  make  PV  equal 
to  P'm',  and  draw  the  straight  line  v'R\  then  PVR'  will  be  the  inclination  of  the 
tangent  plane  at  the  point  O. 

Again  in  OT',  make  O't'  equal  to  0'?n',  and  draw  i'u'  parallel  to  PR'.  From 
O',  with  the  radius  O'R',  describe  an  arc  meeting  t'u'  in  u,  and  draw  the  straight 
line  OV ;  then  t'O'u'  is  the  hypothenuse. 

For  since  P'S'  is  equal  to  P'R',  and  PV  equal  to  P'm',  and  the  angles  m'P'S'^ 
and  f/P'R',  are  right  angles  ;  therefore  the  triangle  v'Y'K'  is  equal  to  the  triangle 
m'P'S',  and  the  remaining  angles  of  the  one,  equal  to  the  remaining  angles  of  the 
other,  each  to  each  ;  hence  the  angle  PVR',  is  equal  to  the  angle  P'm'S'. 

Again,  because  O't?  is  equal  to  O'm',  and  O'Q'  is  equal  to  O'R',  and  OV  is  also 
equal  to  O'R' ;  therefore  OV  is  equal  to  O'Q',  and  since  the  angles  O't'u'  and 
O'm'Q'  are  each  a  right  angle,  therefore  the  two  right  angled  triangles  have  their 
hypothenuses  equal  to  each  other,  and  have  also  one  leg  in  each,  equal  to  each 
other  ;  therefore  the  remaining  side  of  the  one  triangle  is  equal  to  the  remaining 
side  of  the  other,  and  therefore  also  the  angles  which  are  opposite  to  the  equal 
sides  are  equal  ;  hence  the  angle  P'OV  is  equal  to  N'O'Q,'. 

By  considering  this  construction  by  the  transposition  of  the  triangles,  the  whole 
of  the  angles  which  the  tangent  planes  make  at  a  series  of  points  O  in  figures  1 
and  3,  and  their  hypothenuses  may  be  all  found  in  one  diagram,  as  in  figure  4. 

Thus,  in  fig.  4,  if  the  angles  ACO,  ACO',  ACO",  AGO"'  be  respectively  equal 
to  ACO,  ACO',  ACO7,  ACO'",  Jig.  1,  and  in  Jig.  4,  the  semicircle  AO'B  be  de- 
scribed and  if  CD  be  drawn  perpendicular  to  AB,  and  the  angles  CAD,  CBD, 
be  made  equal  to  BCD,  Jig.  1 ;  then  each  half  of  Jig.  4,  being  constructed  as  in 
Jig.  2  ;  the  angles  at  m,  m',  m",  m'",  will  be  respectively  equal  to  the  angle  PmS, 
P'm'S',  Q"m"S",  Q"m'"S'',  in  Jig.  1. 

Also,  in  Jig.  4,  the  angles  CAE,  CAg,  CAh,  CBi,  CBk,  CBF  will  be  the  hypothe- 
nuses at  the  point  A,  O,  O'  O",  O'",  B  in  Jig.  1. 

We  may  here  observe,  Jig.  1,  that  the  angles  which  the  tangent  planes  make 
with  the  plane  of  the  base  in  the  first  quadrant  are  acute  ;  and  those  in  the  second 
quadrant  are  obtuse  ;  and  those  in  the  second  quadrant  are  the  supplements  of 
the  angles  PmS  ;  and,  moreover,  that  all  the  angles  which  constitute  the  hy- 
pothenuses of  the  trehedral,  are  all  acute,  whether  in  the  first  quadrant  or  second 
quadrant  of  the  semicircle  AOB. 


SECTION  II. 

ON  THE  PROJECTION  OF  A  STRAIGHT  LINE  BENT  UPON  A 
CYLINDRIC  SURFACE,  AND  THE  METHOD  OF  DRAWING  A 
TANGENT  TO  SUCH  A  PROJECTION. 

PROBLEM  I. 

Given  the  (level opement  of  the  surface  of  the  serni-cy Under,  and 
a  straight  line  in  that  devel opement,  to  find  the  projection  of  the 
straight  line  on  a  plane  passing  through  the  axis  of  the  cylinder, 
supposing  the  developement  to  encase  the  semi-cylindric  surface. 


76 


OPERATIVE  MASONRY. 


Fg.  5.  Let  ABC  be  the  developement  of  the  cylindric  surface,  BC  being  the 
developement  of  the  semi-circumference,  and  let  AC  be  the  straight  line  given. 

Produce  CB  to  D,  making  BD  equal  to  the  diameter  of  the  cylinder.  On  BD, 
as  a  diameter,  describe  the  semi-circle  BED,  and  divide  the  semi-circular  ?arc 
BED,  into  any  number  of  equal  parts,  at  1,  2,  3,  &c. ;  and  its  developement  BC 
into  the  same  number  of  equal  parts,  at  the  points /,  g,  h,  &c.  Draw  the  straight 
lines  fk,  gl,  hm,  &c.  parallel  to  BA,  meeting  AC  at  the  points  kt  /,  m,  &c. ;  also 
parallel  to  BA,  draw  the  straight  lines  lo,  Sq,  &c.  and  draw  ko,  lp,  mq,  &c. 
parallel  to  CD  ;  and  the  points  o,  p,  q,  &c.  are  the  projections  or  seats  of  the 
points  k,  I,  m,  &c.  in  the  developement  of  the  straight  line  AC. 

The  projection  of  a  screw  is  found  by  this  method  :  BD  may  be  considered  as 
the  diameter  of  the  cylinder  from  which  the  screw  is  formed  ;  and  the  angle 
BAC,  the  inclination  of  the  thread  with  a  straight  line  on  the  surface  ;  or  BCA 
the  inclination  of  the  thread  with  the  end  of  the  cylinder.  The  same  principle 
also  applies  to  the  delineations  of  the  hand-rails  of  stairs,  and  in  the  construc- 
tion of  bevel  bridges. 

PROBLEM  II. 

Given  the  entire  projection  of  a  helix  or  screw,  in  the  surface  of 
a  semi-cylinder,  and  the  projection  of  a  circle  in  that  surface  per- 
pendicular to  the  axis,  upon  the  plane  passing  through  the  axis,  to 
draw  a  tangent  to  the  curve  at  a  given  point. 

Fig.  6.  Let  BPK  be  the  projection  of  the  helix  or  screw,  and  BA  the  pro- 
jection of  the  circumference  of  a  circle,  and  since  this  circle  is  in  a  plane  perpen- 
dicular to  the  plane  of  projection,  it  will  be  projected  into  a  straight  line  AB, 
equal  to  the  diameter  of  the  cylinder. 

On  AB  as  a  diameter,  describe  the  semicircle  ArB,  and  draw  Pr  perpendicu- 
lar to,  and  intersecting  AB  in  q,  join  the  points  e,  r,  and  produce  er  to /. 

Produce  AB  to  C,  so  that  BC  may  be  equal  to  the  semicircular  arc  BrA. 
Draw  CD  perpendicular  to  BC,  and  make  CD  equal  to  AK,  and  draw  the 
straight  line  BD  ;  then  BD  will  be  the  developement  of  the  curve  line  BPK. 

Draw  Pit  parallel  to  AC,  meeting  BD  in  u,  and  draw  ut  perpendicular  to 
BC.  Draw  rg  perpendicular  to  er,  and  make  rg  equal  to  Bt.  Draw  gn  perpen- 
dicular to  AC,  meeting  BC  in  ra,  and  draw  the  straight  line  nP ;  then  nP  will 
touch  the  curve  at  the  point  P. 

Or  the  tangent  may  be  drawn  independent  of  BCD  thus  :  Draw  Pr  perpen- 
dicular to  AB,  and  rg  a  tangent  at  r.  Make  rg  equal  to  the  developement  of  rB, 
and  draw  gn  perpendicular  to  BC,  meeting  BC  in  n,  and  join  nP,  which  is  the 
tangent  required. 


77.  7. 


APPLICATION  OF  GEOMETRY  TO  PLANS,  &c. 


77 


SECTION  III. 

APPLICATION  OF  GEOMETRY  TO  PLANES  AND  ELEVATIONS, 
AND  ALSO  TO  THE  CONSTRUCTION  OF  ARCHES  AND  VAULTS. 

PRELIMINARY  PRINCIPLES  OF  PROJECTION. 

If  from  a  point  A',  Plate  VII.  fig.  1  in  space,  a  perpendicular  A'a 
be  let  fall  to  any  plane  PQ  whatever,  the  foot  a  of  this  perpendicu- 
lar is  called  the  projection  of  the  point  A'  upon  the  plane  PQ. 

If  through  different  points  A,  B',  C,  D'~  .  .  .  .  jigs.  2,  3,  4,  of 

any  line  A'B'C'D'  whatever  in  space,  perpendiculars  A'a,  B'6, 

C'c,  D'd,  be  let  fall  upon  any  plane  PQ  whatever,  and  if 

through  a,  6,  c,  a7,  the  projection  of  the  points  A',  B',  C', 

D',  in  the  plane  PQ  a  line  be  drawn,  the  line  thus  drawn 

will  be  the  projection  of  the  line  A'BC'D'  ....  given  in  space. 

If  the  line  A  BCD'  jig.  3,  be  straight,  the  projection  abed 

.  .  .  .  will  also  be  a  straight  line;  and  if  the  line  A'B'C'D  .  .  .  .fig. 
2,  be  a  curve  not  in  a  plane  perpendicular  to  the  plane  PQ,  the 
curve  abed  ....  which  is  the  projection  of  the  curve  A'B'C'D' 
....  in  space,  will  be  of  the  same  species  with  the  original  curve, 
of  which  it  is  the  projection.  Hence,  in  this  case,  if  the  original 
curve  A'B'C'D  ....  be  an  ellipse,  a  parabola,  hyperbola,  &c,  the 
projection  abed  ....  will  be  an  ellipse,  a  parabola,  an  hyperbola, 
&c.  The  circle  and  the  ellipse  being  of  the  same  species,  the  pro- 
jected curve  may  be  a  circle  or  ellipse,  whether  the  original  be  a 
circle  or  ellipse,  as  in  fig.  4. 

The  plane  in  which  the  projection  of  any  point,  line,  or  plane 
figure  is  situated,  is  called  the  plane  of  projection,  and  the  point  or 
line  to  be  projected  is  called  the  primitive. 

The  projection  of  a  curve  will  be  a  straight  line  when  the  curve 
to  be  projected  is  in  a  plane  perpendicular  to  the  plane  of  projection. 
Hence  the  projection  of  a  plane  curve  is  a  straight  line. 

If  a  curve  be  situated  in  a  plane  which  is  parallel  to  the  plane  of 
projection,  the  projection  of  the  curve  will  be  another  curve  equal 
and  similar  to  the  curve  of  which  it  is  the  projection. 

The  projection  upon  a  plane  of  any  curve  of  double  curvature 
whatever  is  always  a  curve  line. 

In  order  to  fix  the  position  and  form  of  any  line  whatever  in 
space,  the  position  of  the  line  is  given  to  each  of  two  planes  which 
are  perpendicular  to  each  other ;  the  one  is  called  the  horizontal 
plane  and  the  other  the  vertical  plane  ;  the  projection  of  the  line  in 
question  is  made  on  each  of  these  two  planes,  and  the  two  projec- 
tions are  called  the  two  projections  of  the  line  to  be  projected. 

Thus  we  see  in  fig.  5,  where  the  parallelogram  UV WX  represents 
the  horizontal  plane,  and  the  parallelogram  UVYZ  represents  the 
vertical  plane,  the  projection  ab  of  the  line  A'B'  in  space  upon  the 
horizontal  plane  UVWX,  is  called  the  horizontal  projection,  and  the 


78 


OPERATIVE  MASONRY. 


projection  AB  of  the  same  line  upon  the  vertical  plane  UVYZ,  is 
called  the  vertical  projection. 

The  two  planes,  upon  which  we  project  any  line  whatever,  are 
called  the  planes  of  projection. 

The  intersection  UV  of  the  two  planes  of  projection,  is  called  the 
ground  line. 

When  we  have  two  projections  afe,  AB  of  any  line  A  B'  in  space, 
the  line  A'B'  will  be  determined  by  erecting  to  the  planes  of  projec- 
tion the  perpendiculars  «A',  B6' .  .  .  .,  A  A',  BB'  through 

the  projections  a,  6,  ;  A,  B,  of  the  original  points 

A'  B',  .  .  .  .  of  the  line  in  question.  For  the  perpendiculars  aA',  AA 
erected  from  the  projections  a,  A  of  the  same  point  A'  will  intersect 
each  other  in  space  in  a  point  A',  which  will  be  one  of  these  in  the 
line  in  question.  It  is  clear  that  the  other  points  must  be  found  in 
the  same  manner  as  this  which  has  now  been  done. 

When  we  have  obtained  the  two  projections  of  a  line  in  space, 
whether  immediately  from  the  line  itself,  or  by  any  other  means 
whatever,  we  must  abandon  this  line  in  order  to  consider  its  two 
projections  only.  Since,  when  we  design  a  working  drawing,  we 
operate  only  upon  the  two  projections  of  this  line  that  we  have 
brought  together  upon  one  plane,  and  we  no  longer  see  any  thing  in 
space. 

However,  to  conceive  that  which  we  design,  it  is  absolutely 
necessary  to  carry  by  thought  the  operations  into  space  from  their 
projections.  This  is  the  most  difficult  part  that  a  beginner  has  to 
surmount,  particularly  when  he  has  to  consider  at  the  same  time  a 
great  number  of  lines  in  various  positions  in  space. 

The  perpendicular  A'a,  fig.  5,  let  fall  from  any  point  A  whatever 
in  space  upon  the  plane  XV  of  projection,  is  called  the  projectant  of 
the  point  A'  upon  this  plane.  Moreover,  the  perpendicular  distance 
between  the  point  A'  and  the  horizontal  plane  XV,  is  called  the  pro- 
jectant upon  the  horizontal  plane,  or  simply  the  horizontal  project- 
ant; and  the  perpendicular  distance  A'A  between  the  original  point 
A'  and  the  vertical  plane  UY,  is  called  the  projectant  upon  the  ver- 
tical plane,  or  simply  the  vertical  projection. 

We  shall  remark,  so  as  to  prevent  any  mistake,  that  the  horizon- 
tal projectant  A'a,  is  the  perpendicular  let  fall  from  the  original 
point  upon  the  horizontal  plane,  and  that  the  vertical  projectant  is 
the  perpendicular  let  fall  from  that  point  upon  the  vertical  plane. 
Hence  the  horizontal  projectant  is  parallel  to  the  vertical  plane,  and 
is  equal  to  the  distance  between  the  original  point  and  the  horizontal 
plane  ;  and  the  vertical  projectant  is  parallel  to  the  horizontal  plane, 
and  is  equal  to  the  distance  between  the  original  point  and  the  verti- 
cal plane. 

We  may  remark,  that  if  through  a,  fig,  6,  the  horizontal  projec- 
tion of  the  point  A'  we  draw  a  perpendicular  aa  to  UV  the  ground 
line,  this  perpendicular  aa  will  be  equal  to  the  measure  of  the  ver- 
tical projectant  A'A;  consequently  the  distance  of  the  point  A'  to  the 
vertical  plane  is  equal  to  the  distance  between  a,  its  horizontal  pro- 
jection, and  U V  the  ground  line  measured  in  a  perpendicular  to  UV. 
In  like  manner,  if  through  A,  the  vertical  projection  of  the  point  A', 


APPLICATION  OF  GEOMETRY  TO  PLANS,  &c. 


79 


we  draw  a  perpendicular  Art  toUV  the  ground  line,  thisjperpendjQU- 
lar  Art  will  be  equal  to  the  measure  of  the  horizontal  projcctant  Art  ; 
consequently,  the  distance  of  this  point  A'  to  the  horizontal  plane,  is 
equal  to  the  distance  between  A  its  vertical  projection,  and  UV  the 
ground  line  measured  in  a  perpendicular  to  UV. 

To  these  very  important  remarks  we  shall  add  one  which  is  not 
less  so.  Two  perpendiculars,  oa,  fig.  G,  Aa,  being  let  fall  from  the 
projections  a.  A  to  the  same  point  A',  upon  the  ground  line  UV, 
will  meet  each  other  in  the  same  point  a,  of  the  said  ground  line  UV. 

If  we  now  wished  the  two  projections  of  a  point  A',  fig.  6,  or  of 
any  line  A'B'  whatever,  to  be  upon  one  or  the  same  plane,  it  is  sufficient 
to  imagine  the  vertical  plane  UVYZ  to  turn  round  the  ground-line 
UV,  in  such  a  manner  as  to  be  the  prolongation  of  the  horizontal 
plane  UVWX  ;  for  it  is  clear  that  this  plane  will  carry  with  it  the 
vertical  projection  A  or  AB  of  the  point,  or  of  the  line  in  question. 
Moreover  we  see,  and  it  is  very  important  that  the  lines  Aa,  Bh, 
perpendicular  to  the  ground-line  UV  will  not  cease  to  be  so  in  tbe 
motion  of  the  plane  UVYZ  ;  and  as  the  corresponding  lines  rta,  6b, 
are  also  perpendiculars  to  the  ground  line  UV,  it  follows  that  the 
lines  aa',  hb\  will  be  the  respective  prolongation  of  the  lines  «a,  i>b. 

Hence  it  results,  when  we  consider  objects  upon  a  single  plane, 
the  projections  rt,  A  of  the  point  A'  in  space  are  necessarily  upon  tire 
same  perpendicular  Art  to  the  ground-line  UV. 

It  is  necessary  to  call  to  mind  that  the  distance  Aa  measures  the 
distance  from  the  point  in  space  to  the  horizontal  plane,  (the  point 
A  being  the  vertical  projection  of  this  point,)  and  that  the  line  «a 
measures  the  distance  from  the  same  point  in  space  to  the  vertical 
plane. 

It  follows,  that  if  the  point  in  space  be  upon  the  horizontal  plane, 
its  distance  with  regard  to  this  last-named  plane  will  be  zero  or 
nothing,  and  the  vertical  Aa  will  he  zero  also.  Moreover,  the  verti- 
cal projection  of  this  point  will  be  upon  the  ground-line  at  the  foot  a, 
of  the  perpendicular  rta  let  fall  upon  .the  ground-line,  from  the  hori- 
zontal projection  rt  of  this  point. 

Again,  if  the  point  in  space  be  upon  the  vertical  plane,  its  dis- 
tance, in  respect  of  this  plane,  will  be  zero,  the  horizontal  «a  will  be 
zero,  and  the  horizontal  projection  of  the  point  in  question  will  be 
the  foot  a  of  the  perpendicular  Aa  let  fall  upon  the  ground-line  from 
the  vertical  projection  A  of  this  point. 

In  general,  we  suppose  that  the  vertical  projection  of  a  point  is 
above  the  ground-line,  and  that  the  horizontal  projection  is  below.; 
but  from  what  has  been  said,  it  is  evident  that  if  the  point  in  space 
be  situated  below  the  horizontal  line,  its  vertical  projection  will  be 
below  the  ground-line  ;  for  the  distance  from  this  point  to  the  hori- 
zontal plane,  cannot  be  taken  from  the  base-line  to  the  .top,  but  from 
the  top  to  the  base  with  respect  to  its  plane. 

So  if  the  point  in  space  be  situated  behind  the  vertical  plane, 
its  horizontal  projection  will  be  above  the  ground-line,  from  which 
we  conclude — 

1st.  If  the  point  in  question  be  situated  above  the  horizontal  plane, 


11 


80 


OPERATIVE  MASONRY. 


and  before  the  vertical  plane,  its  vertical  projection  will  be  above, 
and  its  horizontal  projection  below  the  ground-line. 

2d.  If  the  point  be  situated  before  the  vertical  plane,  and  below 
the  horizontal  plane,  the  two  projections  will  be  below  the  ground- 
line. 

3d.  If  the  point  be  situated  above  the  horizontal  plane,  but  be- 
hind the  vertical  plane,  the  two  projections  will  be  above  the 
ground-line. 

4th.  Lastly.  If  the  point  be  situated  above  the  horizontal  plane, 
and  behind  the  vertical  plane,  the  vertical  projection  will  be  below, 
and  the  horizontal  projection  above,  the  ground-line. 

The  reciprocals  of  these  propositions  are  also  true. 

If  a  line  be  parallel  to  one  of  the  planes  of  projection,  its  projec- 
tion upon  the  other  plane  will  be  parallel  to  the  ground-line.  Thus, 
for  example,  if  a  line  be  parallel  to  a  horizontal  plane,  its  vertical 
projection  will  be  parallel  to  the  ground  line  ;  and  if  it  is  parallel  to 
the  vertical  plane,  its  horizontal  projection  will  be  parallel  to  the 
ground-line. 

Reciprocally,  if  one  of  the  projections  of  a  line  be  parallel  to  the 
ground  line,  this  line  will  be  parallel  to  the  plane  of  the  other  pro- 
jection. Thus,  for  example,  if  the  vertical  projection  of  a  line  be 
parallel  to  the  ground-line,  this  line  will  be  parallel  to  the  horizon- 
tal plane,  and  vice  versa. 

If  a  line  be  at  any  time  parallel  to  the  two  planes  of  projection,  the 
two  projections  of  this  line  will  be  parallel  to  the  ground-line  ;  and 
reciprocally,  if  the  two  projections  of  a  line  be  parallel  to  the  ground- 
line,  the  line  itself  will  be  at  the  same  time  parallel  to  the  two  planes 
of  projection. 

If  a  line  be  perpendicular  to  one  of  the  planes  of  projection,  its 
projection  upon  this  plane  will  only  be  a  point,  and  its  projection 
upon  the  other  plane  will  be  perpendicular  to  the  ground-line. 
Thus,  for  example,  if  the  line  in  question  be  perpendicular  to  the 
horizontal  plane,  its  horizontal  projection  will  be  only  a  point,  and 
its  vertical  projection  will  be  perpendicular  to  the  ground-line. 

Reciprocally,  if  one  of  the  projections  of  a  straight  line  be  a  point, 
and  the  projection  of  the  other  perpendicular  to  the  ground-line, 
this  line  will  be  perpendicular  to  the  plane  of  projection  upon  which 
its  projection  is  a  point.  Thus  the  line  will  be  perpendicular  to  the 
horizontal  plane,  if  its  projection  be  the  given  point  in  the  hori- 
zontal plane. 

If  a  fine  be  perpendicular  to  the  ground-line,  the  two  projections 
will  also  be  perpendicular  to  this  line.  The  reciprocal  is  not  true  ; 
that  is  to  say,  that  the  two  projections  of  a  line  may  be  perpendicu- 
lar to  the  ground-line,  without  having  the  same  line  perpendicular 
to  the  ground-line. 

If  a  line  be  situated  in  one  of  the  planes  of  projection,  its  projec- 
tion upon  the  other  will  be  upon  the  ground-line.  Thus,  if  a  line 
jhe  situated  upon  a  horizontal  plane,  its  vertical  projection  will  be 
upon  the  ground-line  ;  and  if  this  line  were  given  upon  the  vertical 
plane,  its  horizontal  projection  would  be  upon  the  ground-line. 

Reciprocally,  if  one  of  the  projections  of  a  line  be  upon  the  ground- 
line,  this  line  will  be  upon  the  plane  of  the  other  projection.  Thus, 


APPLICATION  OF  GEOMETRY  TO  PLANS,  &c. 


81 


for  example,  if  it  be  the  vertical  projection  of  the  line  in  question 
which  is  upon  the  ground,  this  line  will  be  upon  the  horizontal 
plane  ;  if,  on  the  contrary,  it  were  upon  the  horizontal  projection  of 
this  line  which  was  upon  the  ground-line,  this  line  would  be  upon 
the  vertical  plane. 

If  a  line  be  at  any  time  upon  the  two  planes  of  projection,  the  two 
projections  of  this  line  would  be  upon  the  ground-line,  and  the  line 
in  question  would  coincide  with  this  ground-line.  Reciprocally,  if 
the  two  projections  of  a  line  were  upon  the  ground-line,  the  line  it- 
self would  be  upon  the  ground-line. 

If  two  lines  in  space  are  parallel,  their  projections  upon  each  plane 
of  projection  are  also  parallel.  Reciprocally,  if  the  projections  of 
two  lines  are  parallel  on  each  plane  of  projection,  the  two  lines  will 
be  parallel  to  one  another  in  space. 

If  any  two  lines  whatever  in  space  cut  each  other,  the  projections 
of  their  point  of  intersection  will  be  upon  the  same  perpendicular 
line  to  the  ground-line,  and  upon  the  points  of  intersection  of  the 
projections  of  these  lines.  Reciprocally,  if  the  projections  of  any 
two  lines  whatever  cut  each  other  in  the  two  planes  of  projection,  in 
such  a  manner  that  their  points  of  intersection  are  upon  the  same 
perpendicular  to  the  ground-line,  these  two  lines  in  question  will 
cut  each  other  in  space. 

The  position  of  a  plane  is  determined  in  space,  when  we  know  the 
intersections  of  this  plane  with  the  planes  of  projection. 

The  intersections  AB,  AC,  of  the  plane  in  question,  with  the 
planes  of  projection,  are  called  the  traces  of  this  plane. 

The  trace  situated  in  the  horizontal  plane  is  called  the  horizontal 
trace,  and  the  trace  situated  in  the  vertical  plane  is  called  the  vertical 
trace. 

A  very  important  remark  is,  that  the  two  traces  of  a  plane  inter- 
sect each  other  upon  the  ground-line. 

If  a  plane  be  parallel  to  one  of  the  planes  of  projection,  this  plane 
will  have  only  one  trace,  which  will  be  parallel  to  the  ground-line, 
and  situated  in  the  other  plane  of  projection.  Reciprocally,  if  a 
plane  has  a  trace  parallel  to  the  ground-line,  this  plane  will  be  par- 
allel to  the  plane  of  projection  which  does  not  contain  this  trace. 
Thus  :— 

1st.  If  a  plane  be  parallel  to  the  horizontal  plane,  this  plane  will 
not  have  a  horizontal  trace,  and  its  vertical  trace  will  be  parallel  to 
the  ground-line.  Likewise,  if  a  plane  be  parallel  to  the  vertical 
plane,  this  plane  will  not  have  a  vertical  trace,  and  its  horizontal 
trace  will  be  parallel  to  the  ground-line. 

2d.  If  a  plane  has  only  one  trace,  and  this  trace  parallel  to  the 
ground-line,  let  it  be  in  the  vertical  plane  ;  then  the  plane  will  be 
parallel  to  the  horizontal  plane.  So  if  the  trace  of  the  plane  be  in 
the  horizontal  plane,  and  parallel  to  the  ground-line,  the  plane  will 
be  parallel  to  the  vertical  plane. 

If  one  of  the  traces  of  a  plane  be  perpendicular  to  the  ground- 
line,  and  the  other  trace  in  any  position  whatever,  this  plane  will  be 
perpendicidar  to  the  plane  of  projection  in  which  the  second  trace 
is.  Thus,  if  it  be  a  horizontal  trace  which  is  perpendicular  to  the 
ground-line,  the  plane  will  be  perpendicular  to  the  vertical  plane  of 


82- 


OPERATIVE  MASONRY. 


projection  ;  and  if,  on  the  contrary,  the  vertical  trace  he  that  which 
is  perpendicular  to  the  ground-line,  then  the  plane  will  be  perpen- 
dicular to  the  horizontal  plane. 

Reciprocally,  if  a  plane  be  perpendicular  to  one  of  the  planes  of 
projection  without  being  parallel  to  the  other,  its  trace  upon  the 
plane  of  projection  to  which  it  is  perpendicular  will  be  to  any  po- 
sition whatever,  and  the  other  trace  will  be  perpendicular  to  the 
ground-line.  Thus,  for  example,  if  the  plane  be  perpendicular  to 
the  vertical  plane,  the  vertical  trace  will  be  in  any  position  whatev- 
er, and  its  horizontal  trace  will  be  perpendicular  to  the  ground-line. 
The  reverse  will  also  be  true,  if  the  plane  be  perpendicular  to  the 
horizontal  plane. 

If  a  plane  be  perpendicular  to  the  two  planes  of  projection,  its 
two  traces  will  be  perpendicular  to  the  ground-line.  Reciprocally, 
if  the  two  traces  of  a  plane  are  in  the  same  straight  line  perpendicu- 
lar to  the  ground-line,  this  plane  will  be  perpendicular  to  both  the 
planes  of  projection. 

If  the  two  traces  of  a  plane  are  parallel  to  the  ground-line,  this 
plane  will  be  also  parallel  to  the  ground-line.  Reciprocally,  if  a 
plane  be  parallel  to  the  ground-line,  its  two  traces  will  be  parallel 
to  the  ground-line. 

When  a  plane  is  not  parallel  to  either  of  the  planes  of  projection, 
and  one  of  its  traces  is  parallel  to  the  ground-line,  the  other  trace  is 
also  necessarily  parallel  to  the  ground-line. 

If  two  planes  are  parallel,  their  traces  in  each  of  the  planes  of 
projection  will  also  be  parallel.  Reciprocally,  if  on  each  plane  of 
projection  the  traces  of  the  two  planes  are  parallel,  the  planes  will 
also  be  parallel. 

If  a  line  be  perpendicular  to  a  plane,  the  projections  of  this  line 
will  be  in  each  plane  of  projection,  perpendicular  to  the  respective 
traces  in  this  plane.  Reciprocally,  if  the  projections  of  a  line  are 
respectively  perpendicular  to  the  traces  of  a  plane,  the  line  will  be 
perpendicular  to  the  plane. 

If  a  line  be  situated  in  a  given  plane  by  its  traces,  this  line  can 
only  intersect  the  planes  of  projection  upon  the  traces  of  the  plane 
which  contains  it.  Moreover,  the  line  in  question  can  only  meet 
the  plane  of  projection  in  its  own  projection.  Whence  it  follows, 
that  the  points  of  meeting  of  the  right  line,  and  the  planes  of  projec- 
tion are  respectively  upon  the  intersections  of  this  right  line,  and 
the  traces  of  the  plane  which  contains  it. 

If  a  right  line,  situated  in  a  given  plane  by  its  traces,  is  parallel  to 
the  horizontal  plane,  its  horizontal  projection  will  be  parallel  to  the 
horizontal  trace  of  the  given  plane,  and  its  vertical  projection  will 
be  parallel  to  the  ground-line.  Likewise,  if  the  right  line  situated 
in  a  given  plane  by  its  traces  is  parallel  to  the  vertical  plane,  its  ver- 
tical projection  will  be  parallel  to  the  vertical  line  of  the  plane 
which  contains  it,  and  its  horizontal  projection  will  be  parallel  to 
the  ground-line. 

Reciprocally,  if  a  line  be  situated  in  a  given  plane  by  its  traces, 
and  that,  for  example,  let  its  horizontal  projection  be  parallel  to  the 
horizontal  trace  of  the  given  plane,  this  line  will  be  parallel  to  the 
horizontal  plane,  and  its  vertical  projection  will  be  parallel  to  the 


SlJ]0!A.CIiS    OF  SOlLIBSo 


DEVELOPEMENTS  OF  THE  SURFACES  OF  SOLIDS.  83 


ground-line.  Likewise,  if  the  vertical  projection  of  the  line  in  ques- 
tion be  parallel  to  the  vertical  trace  of  the  given  plane,  this  line  will 
be  parallel  to  the  vertical  plane,  and  its  horizontal  projection  will 
be  parallel  to  the  ground-line. 


SECTION  IV. 

ON  THE  DEVELOPEMENTS  OF  THE  SURFACES  OF  SOLIDS. 

PROBLEM  I. 

To  find  the  developement  of  the  surface  of  a  right  semi-cylinder. 

Plate  8,  Jig.  1.  Let  ACDE  be  the  plane  passing  through  the  axis.  On  AC, 
as  a  diameter,  describe  the  semicircular  arc  ABC.  Produce  CA  to  F,  and  make 
AF  equal  to  the  developement  of  the  arc  ABC.  Draw  FG  parallel  to  AE,  and 
EG  parallel  to  AF  ;  then  AFGE  is  the  developement  required. 

PROBLEM  II. 

To  find  the  developement  of  that  part  of  a  semi-cylinder  contained 
between  two  perpendicular  surfaces. 

Figs.  2,  3,  4.  Let  ACDE  be  a  portion  of  a  plane  passing  through  the  axis  of 
the  cylinder,  CD  and  AE,  being  sections  of  the  surface,  and  let  DE  and  GF  be 
be  the  insisting  lines  of  the  perpendicular  surface;  also  let  AC  be  perpendicular 
to  AE  and  CD.  On  AC,  as  a  diameter,  describe  the  semi-circular  arc  ABC. 
Produce  CA  to  H,  and  make  AH  equal  to  the  developement  of  the  arc  ABC. 
Divide  the  arc  ABC,  and  its  developement,  each  into  the  same  number  of  equal 
parts  at  the  points  1,  2,  3. 

Through  the  points  1,  2,  3,  &c.  in  the  semi-circular  arc  and  in  its  develope- 
ment, draw  straight  lines  parallel  to  AE,  and  let  the  parallel  lines  through  1,  2, 
3,  in  the  arc  A,  B,  C,  meet  FG  in  p,  q,  r,  &c.  and  AC  in  k,  I,  m,  &c.  Transfer 
the  distances  kp,  Iq,  mr,  &c.  to  the  developement  upon  the  lines  la,  26,  3c,  &c. 
Through  the  points  F,  a,  6,  c,  &c.  draw  the  curve  line  Fcl.  In  the  same  man- 
ner draw  the  curve  line  EK  ;  then  FEKI  will  be  the  developement  required. 

PROBLEM  III. 

To  find  the  developement  of  the  half  surface  of  a  right  cone,  ter- 
minated by  a  plane  passing  through  the  axis. 

Fig.  5.  Let  ACE  be  the  section  of  the  cone  passing  along  the  axes  AE  ;  and 
CE  the  straight  lines  which  terminate  the  conic  surface,  or  the  two  lines  which 
are  common  to  the  section  CAE  and  the  couic  surface  ;  and  let  AC  be  the  line 
of  common  section  of  the  axal  plane,  and  the  base  of  the  cone. 

On  AC  as  a  diameter  describe  a  semi-circle  ABC.  From  E,  with  the  radius 
EA,  describe  the  arc  AF  and  make  the  arc  AF  equal  to  the  semi-circular  arc 
ABC,  and  join  EF  ;  then  the  sector  AEF,  is  the  developement  of  the  portion  of 
the  conic  surface  required. 


84 


OPERATIVE  MASONRY. 


PROBLEM  IV. 

To  find  the  developemerit  of  that  portion  of  a  conic  surface  con- 
tained by  a  plane  passing  along  the  axis,  and  two  surfaces  perpen- 
dicular to  that  plane. 

Fig.  6.  Let  ACE  be  the  section  of  the  cone  along  the  axis,  and  let  AC  and 
GI  be  the  insisting  lines  of  the  perpendicular  surfaces.  Find  the  developement 
AEF  as  in  the  preceding  problem.  Divide  the  semi-circular  arc  ABC,  and  the 
sectorial  arc  AF,  each  into  the  same  number  of  equal  parts  at  the  points  1,  2,  3, 
&c.  From  the  points  1,  2,  3,  &c.  in  the  semi-circular  arc  draw  straight  lines  1£, 
2/,  3m,  &c.  perpendicular  to  AC.  From  the  points  k,  /,  m,  &c.  draw  straight 
lines  &E,  ZE,  mE,  &c.  intersecting  the  curve  AC  in  p,  q,  r,  &c.  Draw  the  straight 
lines  ptt  quf  rv,  &c.  parallel  to  one  side,  EC  meeting  AC  in  the  points  £,  u,  v,  &c. 
Also  from  the  points  1,  2,  3,  in  the  sectorial  arc  AF,  draw  the  straight  lines  IE, 
2E,  3E,  &c.  Transfer  the  distances  pt,  qu,  rv,  &c.  to  la,  26,  3c,  &c;  then 
through  the  points  A,  a,  6,  c,  &c.  draw  the  curve  AcF,  and  AcF  is  one  of  the 
edges  of  the  developement,  and  by  drawing  the  other  edge,  the  entire  develope- 
ment, AGHF,  will  be  found. 


SECTION  V. 

CONSTRUCTION  OF  THE  MOULDS  FOR  HORIZONTAL  CYLIN- 
DRETIC  VAULTS,  EITHER  TERMINATING  RIGHTLY  OR 
OBLIQUELY,  UPON  PLANE  OR  CYLINDRICAL  WALLS,  WITH 
THE  JOINTS  OF  THE  COURSES  EITHER  IN  THE  DIRECTION 
OF  THE  VAULT,  PERPENDICULAR  TO  THE  FACES,  OR  IN 
SPIRAL  COURSES. 

DEFINITIONS  OF  MASONRY,  WALLS,  VAULTS,  &c. 

Stone-cutting  is  the  art  of  reducing  stones  to  such  forms  that 
when  united  together  they  shall  form  a  determinate  whole. 

In  preparing  stones  for  walls,  of  which  their  surfaces  are  intended 
to  be  perpendicular  to  the  horizon,  nothing  more  is  necessary  than 
to  reduce  the  stone  to  its  dimensions,  so  that  each  of  its  eight  solid 
angles  may  be  contained  by  three  plane  right  angles. 

Moreover,  in  working  the  stones  of  common  straight  right  cylin- 
dretic  vaults,  where  the  planes  of  the  sides  of  the  joints  terminate 
upon  the  intrados  or  extrados  of  the  arch  or  vault,  in  straight  lines 
parallel  ruled  lines  of  the  cylindretic  surface,  there  can  be  no  diffi- 
culty ;  for  if  one  of  the  beds  of  the  stone  be  formed  to  a  plane  sur- 
face, and  if  this  side  be  figured  to  the  mould,  and  the  opposite  ends 
squared,  and,  lastly,  the  face  or  vertical  moulds  applied  upon  the 
ends  thus  squared,  and  their  figures  drawn,  these  figures  will  be  the 
two  ends  of  a  prism,  consisting  of  equal  and  similar  figures,  and  will 
be  similarly  situated  ;  and  therefore  we  have  only  to  form  this 
prism,  in  order  to  form  the  arch-stone  required. 


DEVELOPEMENTS  OF  THE  SURFACE  OF  SOLIDS.  85 

But  the  formation  of  the  stones  in  the  angles  of  vaults,  and  in  the 
courses  of  spheretical  niches  and  domes,  are  much  more  difficult, 
and  require  more  consideration.  In  such  constructions  various 
methods  may  be  employed,  and  some  of  these,  in  particular  instan- 
ces, with  great  advantage,  both  in  the  saving  of  workmanship  and 
material,  as  we  shall  have  occasion  to  show.  In  general,  however, 
previous  to  the  reducing  of  a  stone  to  its  ultimate  form  for  such  a 
situation,  it  will  be  found  convenient  to  reduce  the  stone  to  such  a 
figure  as  will  include  the  more  complex  figure  of  the  stone  required, 
so  that  any  surface  of  the  preparatory  figure  may  either  include  a 
surface  or  arris  of  the  stone  required  to  be  formed,  or  be  a  tangent 
to  their  surface. 

Surfaces  are  brought  to  form  by  means  of  straight  and  curved 
edges,  always  applied  in  a  plane  perpendicular  to  the  arris-lines,  so 
that,  when  a  surface  is  thoroughly  formed,  the  edge  of  application 
may  have  all  its  points  in  contact  with  the  surface  in  its  whole  in- 
tended breadth. 

A  wall,  in  masonry,  is  a  mass  of  stones  or  other  material,  either 
joined  together  with  or  without  cement,  so  as  to  have  its  surfaces 
such  that  a  plumb-line,  descending  from  any  point  in  either  face, 
will  not  fall  without  the  solid. 

One  of  the  faces  of  a  wall  is  generally  regulated  by  the  other,  and 
the  regulating  surface  is  called  the  principal  face. 

The  line  of  intersection  of  the  principal  face  of  a  wall,  and  a  hori- 
zontal plane  on  a  level  with  the  ground,  or  as  nearly  so  as  circum- 
stances will  permit,  is  called  the  base-line. 

A  horizontal  section  of  a  wall,  through  the  base-line,  is  called 
the  seat  of  the  wall. 

The  other  side  of  the  seat  of  a  wall,  opposite  to  the  base-line,  is 
called  the  rear-line. 

In  exterior  walls  the  outer  surface  is  always  the  principal  face, 
and  the  base  and  rear-lines  are  generally  so  situated,  that  normals 
drawn  to  the  base-line,  between  the  base  and  rear-lines,  are  all  espial 
to  one  another.  This  uniformity  most  frequently  takes  place  also 
in  partition  or  division  walls  ;  but,  in  some  instances,  on  account  of 
a  room  being  circular  or  elliptical,  while  the  other  faces  are  plane 
or.  curved  surfaces,  this  equality  of  the  normals  cannot  subsist. 

If  a  wall  be  cut  by  a  plane  perpendicular  to  the  base-line,  or  if  the 
base-line  be  a  curve  perpendicular  to  a  tangent  through  the  point  of 
contact,  such  a  section  is  called  a  rigid  section. 

Hence,  according  to  this  definition,  since  the  base-line  is  always 
in  a  horizontal  plane,  every  straight  line  and  every  tangent  to  a 
base-line,  when  it  is  a  curve,  will  be  a  horizontal  line,  therefore  the 
right  section  must  be  in  a  vertical  plane. 

Walls  are  denominated  according  to  the  figure  of  their  base-line. 
When  the  base-line  is  straight,  the  wall  is  said  to  be  straight. 
Hence,  if  the  figure  of  the  base  be  an  arc  or  the  whole  circumfer- 
ence of  a  circle,  or  a  portion  or  the  entire  curve  of  an  ellipse,  the 
wall  is  said  to  be  circular  or  elliptical.  Other  forms  seldom  occur 
in  building. 

Walls  are  more  strictly  defined  by  the  joint  consideration  of  the 
figures  of  their  bases  and  right  section. 


86 


OPERATIVE  MASONRY. 


When  the  base  and  the  right  section  of  a  wall  are  each  a  straight 
line,  and  all  the  horizontal  sections  straight  lines,  the  face  of  the 
wall  is  called  a  ruler  surface,  and  if  all  the  right  sections  have  the 
same  inclination,  the  wall  is  called  a  straight  inclined  wall  ;  if  they 
are  all  vertical,  the  wall  is  called  an  erect  straight  wall,  or  a  verti- 
cal straight  wall.  If  the  right  sections  vary  their  inclination,  the 
wall  is  called  a  winding  wall. 

When  the  base  line  is  the  circumference  or  any  arc  of  a  circle,  and 
the  right  section  a  straight  line  perpendicular  to  the  horizon,  the 
wall  is  said  to  be  cylindric.  If  the  right  sections  of  a  wall  be  all 
equally  inclined  to  the  horizon,  the  wall  is  said  to  be  conic  ;  and 
thus  a  wall  takes  also  the  name  by  which  its  surface  is  called  ;  hence 
a  straight  wall,  which  has  its  right  sections  either  vertical  or  at  the 
same  inclination,  is  called  a  plane  wall. 

A  wall  in  tallus,  or  a  battering  wall,  is  that  of  which  the  vertical 
section  of  the  principal  face  is  a  straight  line  not  perpendicular  to 
the  horizon.    This  vertical  section  is  called  the  tallus-line. 

The  horizontal  distance  between  the  foot  of  the  tallus-line  and  the 
plumb-line,  passing  through  its  upper  extremity,  is  called  the  quanti- 
ty of  batter  ;  and  the  plumb-line,  from  the  top  of  the  tallus-line  to 
the  level  of  its  foot,  is  called  the  vertical  of  the  batter. 

The  interstices  between  the  stones,  for  the  insertion  of  cement  or 
mortar,  in  order  to  connect  the  stones  into  one  solid  mass,  are  called 
joints,  and  the  surfaces  of  the  stones  between  which  the  mortar  is  in- 
serted, are  called  the  sides  of  the  joints. 

When  the  sides  of  the  joints  are  everywhere  perpendicular  to  the 
face  of  a  wall,  and  terminate  in  horizontal  planes  upon  that  face, 
such  joints  are  called  coursing  joints;  and  the  row  of  stones  between 
every  two  coursing  joints,  is  called  a  course  of  stones. 

An  arch  or  vault,  in  masonry,  is  a  mass  of  stones  suspended  over 
a  hollow,  and  supported  by  one  or  more  walls  at  its  extremities,  the 
surface  opposed  to  the  hollow  being  concave,  and  such  that  a  verti- 
C-a^Une,  descending  from  any  point  in  the  curved  surface,  may  not 
meet,  the  curved  surface  in  r.nother  point. 

The  concave  surface  under  the  arch  or  vault,  is  called  the  intrados 
of  that  arch  or  vault  ;  and  if  the  upper  surface  be  convex,  this  con- 
vex surface  is  called  the  extrados. 

Those  joints  which  terminate  upon  the  intrados  in  horizontal 
lines,  are  called  coursing  joints,  and  the  coursing  joints  will  either  be 
straight,  circular,  or  elliptic,  accordingly  as  the  horizontal  sections 
of  the  intrados  are  straight,  circular,  or  elliptic. 

Whether  in  walling  or  in  vaulting,  the  joints  of  the  stones  should 
always  be  perpendicular  to  the  face  of  the  wall,  or  to  the  intrados  of 
the  arch,  and  the  joints  between  the  stones  should  either  be  in  planes 
perpendicular  to  the  horizon,  or  in  surfaces  which  terminate  upon 
the  face  of  the  wall  or  intrados  of  a  vault  in  horizontal  planes  ;  these 
positions  being  necessary  to  the  strength,  solidity,  and  durability  of 
the  work. 

Walls  and  vaults  being  of  various  forms  ;  viz.  straight,  circular, 
and  elliptic,  depending  on  the  plan  of  the  work  ;  hence  the  con- 
struction will  depend  upon  the  simple  figure  or  upon  the  complex 
figure  when  combined  in  two. 


ON  OBLIQUE  ARCHES. 


87 


SECTION  VI. 
ON  OBLIQUE  ARCHES. 
PROBLEM  I. 

To  execute  an  oblique  cylindroidic  arch,  intersecting  each  side  of 
the  wall  in  a  semi-circle,  the  imposts  of  the  arch  being  given. 

Let/o-.  l,  piate  IX,  be  the  elevation,  and  in  Jig.  2,  let  ABCD,  EFGH,  be  the 
two  imposts  which  are  equal  and  similar  parallelograms,  having  the  sides  AB, 
FE  one  of  each  in  a  straight  line,  and  the  sides  DC  and  GH  in  a  straight  line. 

Join  GC,  and  on  GC  as  a  diameter,  describe  the  semi-circle  GIC,  which,  if 
conceived  to  be  turned  upon  the  line  GC  as  an  axis,  until  its  plane  become  per- 
pendicular to  the  seat  BCGF  of  the  soffit  of  the  arch,  it  will  be  placed  in  its  due 
position.  Divide  the  semi-circular  arc  CJG  into  as  many  equal  parts  as  the  ring- 
stones  are  to  be  in  number.  We  shall  here  suppose  there  are  to  be  nine  ring- 
stones.  From  the  points  of  division,  1,  2,  3,  &c.  draw  ordinates  perpendicular 
to  GC,  meeting  GC  in  the  point  p,  q,  r,  &c.  Perpendicular  to  CB,  the  jamb-line 
of  the  impost,  draw  the  lines  pi,  q2,  rS,  &c.  ;  from  the  point  C  as  a  centre,  with 
the  chord  of  one-ninth  part  of  the  semi-circular  arc,  CIG',  describe  an  arc  inter- 
secting pi  CB  at  1  ;  from  the  point  1,  with  the  same  radius  describe  an  arc  inter- 
secting the  line  q2,  in  the  point  2  ;  from  the  point  2  as  a  centre  with  the  same 
radius,  describe  an  arc  intersecting  the  line  r3,  in  the  point  3  ;  and  so  on.  Join 
the  point  C  and  1  ;  1  and  2;  2  and  3,  &c.  and  thus  form  the  entire  edge  CKL,  of 
the  devolopement  of  the  semi-circular  arc  CIG. 

Through  the  points  1,  2,  3,  &c.  in  CKL,  draw  the  lines  1%  2y,  3f,  &c,  par- 
allel to  CB,  and  make  1/3,  2y,  3<T,  &c.  each  equal  to  CB ;  and  join  Bfi,  fry,  y£ 
&c. ;  then  CB01  is  the  soffit  of  the  first  ring-stone  ;  1/3^2,  is  the  soffit  of  the 
second  ring-stone  ;  2^  3,  the  soffit  of  the  third  ring-stone,  and  so  on. 

Perpendicular  to  GF  draw  FJ  ;  produce  CB  to  J  ;  and  parallel  to  CJ,  drawls, 
qt,  ru,  &c.  Intersecting  FJ  in  the  points  v,  w,  x,  &c,  make  vs,  wt,  xu,  &c, 
respectively  equal  to  pi,  q2,  r3,  &c.  Join  J  and  s,  s  and  t,  t  and  u,  &c. ;  and 
complete  the  polygonal  line  JwF.  Through  the  points  s,  t,  u,  &e.  draw  the  joint 
lines  sy,  tz,  wo,  radiating  to  the  point  o  ;  then  will  the  angles  of  inclination  of  the 
beds  and  soffits  be  NJs,  ysJ,  the  first  ring-stone ;  yst,  zts,  for  the  second  ring- 
itone  ;  ztu9  Out  for  the  third  ring-stone  ;  and  so  on. 

From  any  point  B  in  EC,  fig.  3,  make  the  angle  CBA  equal  to  the  angle  ABC, 
of  the  impost  Jig.  2.  Prolong  CB  to  E.  From  B  as  a  centre,  with  any  radius 
describe  the  semi-circular  arc  CDE ;  and  on  BC  as  a  diameter,  describe  another 
semi-circular  arc  Cg-B.  Divide  the  semi-circular  arc  CDE,  in  the  points  1,  2,  3, 
&c  into  nine  equal  parts,  equal  to  the  number  of  ring-stones,  and  draw  the 
radials  IB,  2B,  3B,  &c.  intersecting  the  semi-circular  arc  GgB  in  the  points/,  g-, 
h,  &c.  Draw  CA  perpendicular  to  BC  ;  and  in  BA  as  a  diameter,  describe  the 
same  circular  arc  BCA,  From  the  point  B,  with  the  radii  B/,  Bg,  Bh,  &c.  de- 
scribe the  arcs  fi,  gk,  hi,  &c.  meeting  the  semi-circular  arc  BCA,  in  the  points  i,  k, 
I,  &c,  and  draw  the  straight  lines  Bi,  B&,  Bl,  &c.  Then,  ABC  being  the  angle 
of  the  impost,  ABi'  will  be  the  angle  of  the  joints  at  the  junction  of  the  first  and 
\2 


83  OPERATIVE  MASONRY. 

second  ring-stones  ;  ABA:  the  angle  of  the  joints  at  the  junction  of  the  second 
and  third  ring-stones ;  ABl  will  be  the  angle  of  the  joints  at  the  junction  of  the 
third  and  fourth  ring-stones,  &c. 

To  apply  the  moulds  for  cutting  any  one  of  the  ring-stones,  or  to  form  the 
solid  angles  made  by  the  face,  the  two  beds  and  the  soffit  of  the  stone,  which 
being  done  will  form  that  ring-stone. — For  instance,  let  it  be  required  to  form 
the  third  ring-stone  : — We  have  given  the  plain  angle  2}<f,  figure  2,  which  is  a 
side,  and  the  piano  angle  ABk  fig.  3,  another  adjacent  side  ;  also  the  angle  ztu, 
fig.  2,  which  is  the  inclination  of  these  two  sides,  to  construct  the  solid  angle. 
This  can  be  easily  done  by  working  the  bed  of  the  stone  corresponding  to  the 
joint  2y  on  the  soffit  fig.  2  ;  then  work  the  narrow  side  of  the  stone,  from  which 
the  soffit  is  to  be  formed,  first  as  a  plane  surface,  making  an  angle  ztu,  with  the 
bed  first  wrought;  place  the  surface  of  the  mould  abed,  fig.  4,  upon  the  narrow 
side  of  the  stone,  which  is  to  form  the  soffit,  so  that  the  edge  ab  may  be  upon 
the  arris  of  the  stone  ;  then  by  the  edge  be,  draw  a  line  :  again,  upon  the  wrought 
side  which  is  intended  for  the  bed,  apply  the  angle  ABA;,  fig.  3,  so  that  the  line 
AB  may  be  upon  the  arris,  and  the  point  B  upon  the  same  point  that  b  was  ap- 
plied ;  then  by  the  leg  BAr,  which  is  supposed  to  be  upon  the  surface  of  the  bed> 
draw  a  line  ;  we  have  only  to  cut  away  the  superfluous  stone  on  the  outside  of 
the  two  lines  on  the  bed  and  on  the  soffit ;  and  thus  we  shall  form  a  complete 
trehedral ;  the  plane  soffit  of  the  stone  being  gauged  to  its  breadth,  and  the 
mould  2ed3,  fig.  1,  being  applied  upon  the  last  wrought  side,  so  that  the  points 
d,  c,  may  be  upon  the  points  of  the  stone  to  which  b  and  c  were  applied  ;  then 
drawing  a  line  by  the  edge  d3,  and  cutting  away  the  superfluous  stone  between 
the  two  lines  on  the  front,  and  on  the  plane  of  the  soffit,  will  form  the  upper  bed 
of  the  stone. 

This  will  be  made  sufficiently  evident  by  a  developement  of  the  soffit,  the  two 
beds,  and  the  front  of  the  ring-stone.  Make  an  equal  and  similar  parallelogram 
abed, fig.  4,  to  that  of  2^3,  fig.  2.  Make  the  angles  abe,  deg,  fig.  4,  respectively 
equal  to  the  angles  ABA;,  ABl,  fig.  3  ;  then  be  being  equal  to  de,fig.  1,  apply  the 
mould  2de3,  so  that  the  points  d,  e  may  be  upon  be,  fig.  4,  and  draw  the  front  of 
the  stone  bcki  fig.  4,  and  similarly  draw  adml.  Make  be  equal  to  bi,  eg  equal  to 
ck,  and  draw  ef  and  gh  parallel  to  ba  or  cd,  and  this  will  complete  the  develope- 
ment. 

A  complete  model  of  the  stone  will  instantly  be  formed,  by  revolving  the  four 
sides  a&e/,  bcki,  cdhg,  dalm,  upon  the  four  lines  ba,  be,  cd,  da  as  axes,  until  c  coin- 
cide with  i,  k  with  g,  h  with  m,  and  I  with  /. 

We  have  here  made  use  of  the  developement  of  the  intrados  in  the  construc- 
tion of  the  solid  angles,  as  being  easily  comprehended.  The  ring-stones  might, 
however,  have  been  formed  by  the  angle  of  the  joints,  which  is  one  side  of  a  tre- 
hedral; one  of  the  angles  of  the  face  mould,  which  is  the  other  adjacent  side  ; 
and  the  inclination  of  these  two  sides  ;  so  that  we  shall  have  here  also  two  sides 
and  the  contained  angle,  to  construct  the  solid  angle  of  the  trehedral.  As  an 
example,  let  it  again  be  required  to  construct  the  third  ring-stone.  To  find  the 
angle  which  the  face  of  the  third  ring-stone  makes  with  the  bed  in  the  second 
joint :  we  have  here  given  the  two  legs  ABC,  CB2,  fig.  3,  of  a  right-angled 
trehedral,  to  find  the  angle  which  the  hypothenuse  makes  with  the  side  CB2: 
this  being  found,  will  be  the  inclination  of  the  face-mould,  2de3,fig.  1,  and  ABA: 
Jig.  3,   Therefore,  in  this  case  work  the  bed  of  the  stone  first,  then  t^ie  face, 


r 


ON  OBLIQUE  ARCHES. 


80 


to  the  angle  of  inclination  thus  found.  Upon  the  arris  apply  the  leg  AB  of  the 
joint-mould  ABA;,  Jig.  3,  so  that  the  side  Bk  may  be  upon  the  bed,  and  draw  a 
straight  line  on  the  bed  by  the  edge  Bk ;  next  apply  the  mould  2de'3,  so  that  the 
arc  d2  may  be  upon  the  arris,  and  the  point  d  upon  the  same  point  of  the  arris 
to  which  the  point  B  was  applied,  and  the  chord  de  upon  the  face  ;  then  draw  a 
line  on  the  face  of  the  stone,  by  the  leg  de ;  and  work  off  the  superfluous  stone, 
and  the  face  will  be  exhibited.    Fig.  5,  shows  the  stone  as  wrought. 

From  what  has  been  said,  it  is  evident  that  if  one  of  the  solid  angles  of  a  ring- 
stone  be  formed  of  an  oblique  arch  in  a  straight  wall,  the  remaining  solid  angle 
may  be  formed  without  the  use  of  the  trehedral.  Thus,  for  instance,  suppose  the 
solid  angle  which  is  formed  be  made  by  the  surface  of  the  soffit,  the  bed,  and  the 
face  of  the  arch — we  have  only  to  guage  the  soffit  to  its  breadth,  and  apply  the 
head-mould  upon  the  face  of  the  stone  ;  then  by  working  off  the  superfluous 
stone  between  these  lines,  another  solid  angle  will  be  formed  by  the  surface  of 
the  soffit,  the  upper  bed  of  the  stone,  and  the  face  of  the  arch. 

And  since  the  angle  of  the  joints  is  the  same  in  the  lower  and  upper  beds  of 
any  two  ring-stones  that  come  in  contact  with  each  other,  the  same  angle  of  the 
joints  will  do  for  both,  so  that  in  fact,  if  this  be  carried  from  one  ring-stone  to 
another,  the  arch  may  be  executed  without  any  joint  mould. 

This  mode  would,  however,  not  only  be  inconvenient,  but  liable  to  very  great 
inaccuracy.  It  would  be  inconvenient,  as  it  is  necessary  to  work  one  stone  be- 
fore another,  so  that  only  one  workman  could  be  employed  in  the  construction 
of  the  arch.  It  would  be  liable  to  inaccuracy  when  the  number  of  ring-stones 
are  many,  for  then  any  small  error  would  be  liable  to  be  multiplied  or  transmitted 
from  one  stone  to  another.  Besides,  it  is  satisfactory  to  have  a  mould  to  apply, 
in  order  to  examine  the  work  in  its  progress. 

What  has  been  now  observed,  with  regard  to  the  oblique  arch  in  a  straight 
wall,  and  with  respect  to  the  angle  on  the  edges  of  the  point,  will  apply  to  every 
arch  of  which  the  intrados  is  a  cylindric  or  cylindroidic  surface. 

In  the  construction  of  any  object  it  is  always  desirable  to  have  two  different 
methods,  as  one  may  always  be  a  proof  or  check  to  the  other.  Besides,  though 
these  methods  may  be  equally  true  in  principle,  one  of  them  may  be  often  liable 
to  greater  inaccuracy  in  its  construction  than  the  other. 

PROBLEM  II. 

To  construct  the  moulds  for  a  cylindretic  oblique  arch  termin- 
ating upon  the  face  of  a  wall  in  a  plane  at  oblique  angles  to  the 
springing  plane  of  the  vault,  so  th at  the  coursing  joints  may  be  in 
planes  parallel  to  the  ruller  lines  of  the  intrados  of  the  vault. 

Let  the  vertical  plane  of  projection  be  perpendicular  to  the  axis  of  the  intrados, 
and  it  will  therefore  be  also  perpendicular  to  all  the  joints  of  which  their  planes 
are  parallel  to  the  axis:  hence 

The  vertical  projection  of  the  intrados  will  be  a  curve  equal  and  similar  to  the 
curve  of  the  right  section  of  the  intrados. 

The  vertical  projections  of  the  coursing  joints  will  be  radiant  straight  lines,  in- 
tersecting the  curve  lined  projection  of  the  inn-ados. 

The  vertical  projections  of  all  the  joints  which  are  in  vertical  planes  parallel 
to  the  axis,  will  be  straight  lines  perpendicular  to  the  ground  line. 


90 


OPERATIVE  MASONRY. 


The  vertical  projection  of  all  the  joints  m,  horizontal  planes,  will  be  straight 
lines  parallel  to  the  ground-line. 

Moreover,  the  vertical  projections  of  the  intersections  of  planes  which  are  par- 
allel to  the  axis  will  be  points. 

The  horizontal  projections  of  the  planes  of  the  coursing  joints,  and  of  all  the 
intersections  of  the  planes  of  all  joints  which  are  parallel  to  the  s  is,  will  be 
straight  lines  perpendicular  to  the  ground-line. 

And  because  the  axis  of  the  archant  is  perpendicular  to  the  vertical  plane,  the 
vertical  projections  of  the  intrados,  and  of  the  joints  which  are  parallel  to  the 
axis,  will  have  the  same  position  to  one  another,  as  the  curve  and  other  lines 
in  the  right  section  which  are  formed  by  the  joints  in  planes  parallel  to  the  axis. 

All  sections  which  are  perpendicular  to  the  horizon,  will  have  straight  lines 
for  their  horizontal  projections. 

The  length  of  any  inclined  line  will  be  to  the  length  of  its  projection,  as  the 
radius  is  to  the  cosine  of  the  line's  inclination  to  the  plane  of  projection. 

We  shall  suppose  that  the  stones  which  constitute  the  intrados  of  the  archant, 
have  not  fewer  than  three,  nor  more  than  four,  of  their  faces  that  intersect  the 
intrados.  The  stones  which  form  the  face  of  the  archant,  when  they  do  not 
reach  the  rear  of  the  vault,  have  three  of  their  faces  which  intersect  the  intra- 
dos, and  three  at  least  which  intersect  the  face. 

We  shall  call  all  these  surfaces  which  intersect  the  intrados  or  face  of  the  ar- 
chant, the  retreating  sides  of  joints  of  the  stones;  and  the  surface  of  any  stone 
which  forms  a  part  of  the  intrados,  the  douelle  of  the  stone. 

When  the  stones  do  not  reach  from  the  front  to  the  rear  of  the  intrados  of  an 
archant,  they  are  arranged  in  rows,  in  such  a  manner,  that  the  stones  which 
constitute  any  one  of  the  rows,  have  as  many  of  their  retreating  sides  as  there 
are  stones  in  the  row,  in  one  continued  surface,  and  the  opposite  retreating  sides 
of  all  the  stones  in  another  continued  surface,  while  the  heads  form  a  portion  of 
the  intrados  extending  from  front  to  rear  of  the  vault,  and  the  remaining  re- 
treating sides  of  the  stones  either  come  in  contact,  or  are  connected  together  by 
mortar. 

Every  such  row  of  stones  is  called  a  course  of  vaulting. 

One  course  may  be  joined  to  another  by  bringing  their  adjacent  continued  sur- 
faces in  contact ;  but  they  are  generally  cemented  with  mortar,  which  is  called 
the  coursing  joint,  and  as  this  cementing  substance  should  be  as  thin  as  possible^ 
and  of  an  equal  thickness,  we  shall  suppose  that  the  coursing  joints  intersect  the 
intrados  in  lines,  extending  from  front  to  rear  of  the  vault,  we  shall  call  these 
lines  the  coursing  lines  of  the  intrados. 

in  this  example,  as  the  vertical  projection  of  the  intrados,  and  of  the  joints 
which  are  in  planes  parallel  to  the  axis,  are  identical  in  all  respects  to  the  lines 
of  the  right  section,  the  dimensions  between  every  two  corresponding  points 
being  equal  in  both,  we  may  therefore  substitute  at  once  the  right  section  for  the 
vertical  projection,  placing  the  right  section  upon  the  ground-line  UV. 

Plate  X.  Let  No.  1  be  the  right  section  placed  in  the  situation  of  the  vertical 
plane  projection  upon  the  ground-line  UV,  the  curve-line  COC  being  the  verti- 
cal projection  of  the  intrados,  ADrBF,  CH,  the  projections  of  the  vertical  pro- 
jection coursing  joints,  meeting  the  projection  of  the  intrados  in  the  points  A,  B, 
C.  Of  these  radiant  lines  CH  is  the  projection  of  the  springing.  The  line  BF 
meets  the  line  FG  parallel,  and  EF  perpendicular  to  the  ground-line  UV.  The 


ON  OBLIQUE  ARCHES. 


91 


extrados  ZEDY  of  this  section  is  a  straight  line  parallel  to  the  ground-line.  As 
this  right  section  of  this  vault  is  symmetrical,  We  shall  only  describe  one  half, 
the  other  will  be  understood  by  the  same  rules. 

Let  rs,  No.  2,  be  the  trace  of  the  vertical  face  of  the  wall  on  the  horizontal  plane 
of  projection,  making  a  given  angle  with  the  ground-line  UV,  and  let  uv  and  rs 
be  the  traces  of  the  inclined  face  of  the  wall;  the  inclination  of  this  face  being 
given  by  a  right  section  of  the  wall. 

Let  TAAn,  No.  3,  be  the  right  section  of  the  wall,  of  which  An,  the  base,  is 
equal  to  the  shortest  distance  between  the  two  traces  uv  and  rs,  No.  2,  of  the 
faces  of  the  wall.  The  line  nr  of  this  section,  is  the  section  of  the  vertical 
face,  and  AA,  that  of  the  inclined  face  of  the  wall. 

This  section  TAAn,  No.  3,  is  so  situated,  that  the  base  line  An  is  perpendic- 
ular to  the  traces  uv,  rs,  of  the  faces  of  the  wall,  No.  2,  the  point  n  being  in  the 
line  rs  or  sr  prolonged,  therefore  the  point  A  in  the  line  uv,  orvu  prolonged,  and 
m'  being  perpendicular  to  An  will  be  in  the  same  straight  line  with  the  hori- 
zontal trace  rs  of  the  vertical  face  of  the  wall. 

In  order  to  obtain  the  projection  of  the  intersection  of  the  intrados  and  of 
the  joints  which  are  in  planes  parallel  to  the  axis  of  the  intrados  with  the  inclined 
face  of  the  wall;  we  must  find  the  projection  of  every  line  in  this  inclined  face 
made  by  the  intersection  of  a  horizontal  plane  passing  through  every  point  in  the 
right  section  which  is  formed  by  every  two  lines  in  its  construction. 

For  this  purpose  it  will  be  necessary  to  find  the  horizontal  projection  of  every 
point  of  the  lines  where  the  intersections  of  the  planes  parallel  to  the  axis  meet 
the  inclined  face  of  the  wall.    To  proceed: — 

Take  all  the  heights  of  the  points  of  the  right  section,  and  apply  them  respec- 
tively from  the  point  n  in  the  line  nr  No.  3  ;  through  these  points  draw  lines 
parallel  to  An,  so  that  each  line  may  meet  the  sloping  line  AA.  From  each  of  the 
points  in  the  line  AA  draw  lines  parallel  to  the  horizontal  trace  uv,  No.  2,  and 
lines  being  drawn  from  the  corresponding  points  of  the  right  section  will  give 
the  points  required  by  the  intersection  of  the  two  systems  of  parallel  lines. 

Thus  to  find  the  horizontal  projection  of  the  intersection  of  any  particular  line 
which  is  parallel  to  the  axis  with  the  inclined  face  of  the  wall,  this  line  being 
given  by  its  intersecting  point  in  the  right  section,  No.  1 ;  this  point  being  the 
intersection  of  one  of  the  coursing  lines,  viz.  the  first  A  from  the  middle  of  the 
section,  No.  1. 

Draw  Aa  perpendicular  to  the  ground-line,  and  transfer  the  height  KA  of  the 
point  A,  No.  1,  upon  the  line  nr,  No.  3,  from  II  to  1.  Draw  1-2  parallel  to  IIa, 
AA  meeting  PQ  in  2.  From  2  draw  2a  parallel  to  either  of  the  horizontal  traces 
uv,  or  rs,  No.  2,  and  the  point  a  (No.  2)  is  the  horizontal  projection  of  the  ex- 
tremity of  the  coursing  line  of  the  intrados  which  passes  through  the  point  A 
of  the  right  section. 

In  the  same  manner  may  be  found  the  projections  b  and  c  of  the  intersections 
of  the  coursing  joints  of  the  intrados,  with  the  face  of  the  archant,  and  also  those 
of  the  intersections  of  the  planes  parallel  to  the  axis :  the  projections  of  these 
points  being  exhibited  by  Italic  letters  corresponding  to  those  of  the  Roman  in 
the  right  section. 

To  find  the  developement  of  the  intrados  or  soffit  of  the  arch. 

Parallel  to  the  ground-line  in  No.  2,  draw  the  regulating  line  «fg  in  the  hori- 
zontal plane  of  projection,  intersecting  the  projections  aa',  bb',  cc',  &c.  of  the 
coursing  joint-lines  in  the  points  a,  0,  y,  &c. 


92 


OPERATIVE  MASONRY. 


In  any  convenient  situation,  No.  4,  draw  the  line  VW,  and  in  VW  take  any 
convenient  point  o.  In  oV  make  oa  equal  to  OA,  No.  1,  the  half-chord  of  the 
arc  of  the  section  of  the  key-course  ;  and  in  No.  4,  make  a/3,  fiy,  &c.  equal  to 
the  succeeding  chords  AB,  BC,  &c.  No.  1,  of  the  sections  of  the  courses  in  in- 
trados. 

Through  the  points  a,  0t  y,  No.  4,  draw  the  lines  aa',  bb',  cc',  perpendicular  to 
VW,  and  make  aa,  fib,  yc,  respectively  equal  to  aa,  fib,  yc,  No.  2,  as  also  aa', 
fib',  y'c,  No.  4,  equal  to  aa',  fib',  yd,  No.  2.  In  No.  4,  join  ab,  be,  on  the  one  side, 
and  a'b',  b'c',  on  the  other;  then  aa'b'b,  bb'  c' c,  will  be  the  chord-planes  of  the 
soffits  of  the  courses  of  the  stones  on  each  side  of  the  key-course.  The  figures 
of  the  chord-planes  of  the  right-hand  side  of  the  arch  being  found  in  the  same 
manner,  will  give  the  entire  developement  of  the  intrados  by  joining  the  corres- 
ponding ends  of  the  chord-plane  of  the  key-course. 

Through  any  convenient  point  V,  No.  4,  in  the  line  VW,  draw  ac'  perpendicu- 
lar to  VW,  and  prolong  WV  to  D.  Make  VD  equal  to  AD,  No.  1,  and  through 
D,  No.  4,  draw  dd'  parallel  to  ac.  In  ac,  No.  4,  make  Va,  Va',  respectively  equal 
to  aa,  aa',  No.  2,  and  make  Dd,  Dd',  No.  4,  respectively  equal  to  Id,  Id',  No.  2. 
Join  ad,  ad',  then  will  aa'  d'd,  No.  4,  be  the  side  or  figure  of  the  coursing  joint 
corresponding  with  the  line  AD,  No.  1.  In  the  same  manner  the  remaining  fig- 
ures bbT f,  cc/h'h,  will  be  found,  as  also  the  remaining  figures  of  the  coursing- 
joints  on  the  right-hand  side. 

Then  the  figures  of  the  moulds  for  the  course  of  stones,  of  which  the  right 
section  is  a  figure  equal  and  similar  to  ABFED,  No.  1,  are  No.  1,  and  aa'b'b, 
aa'd'd,  bb'flf,  No.  4.  All  the  stones  are  wrought  to  the  form  of  right  prisms  be- 
fore the  heads  in  the  front  and  rear  of  the  arch  are  formed,  then  the  moulds  of 
the  upper  and  lower  beds  are  applied,  and  their  figures  are  drawn  upon  the  sur- 
faces of  the  coursing-joints,  so  as  to  give  the  intersections  of  the  coursing-joints 
with  the  face  of  the  arch. 

In  the  course  of  stones,  on  the  left  hand  next  to  the  key-course  aa'b'b,  No.  4, 
is  the  chord-figure  of  the  intrados,  aa'd'd,  No,  4,  the  upper-bed,  and  bb'Pf  the 
lower  bed. 

To  find  any  point  in  the  oblique  face  of  the  arch.  Let  the  point 
to  be  found  be  the  point  corresponding  to  the  point  A. 

The  place  of  the  point  A  in  the  oblique  line  aa,  No.  3,  is  at  the  point  2,  and 
its  place  upon  the  projection  No.  2,  is^at  a.  Draw  at,  perpendicular  to  av,  or  to 
uv,  and  in  AT  make  a2,  equal  to  a2  in  aa.  From  the  point  2,  in  at,  draw 
2p  parallel  to  uv,  and  draw  ap  perpendicular  to  uv,  and  the  point  p  will  be  in  the 
curve  of  the  oblique  face  of  the  arch. 

In  the  same  maimer  will  be  found  the  points  i,  q,  &c.  in  the  curve  of  the 
oblique  face  of  the  arch,  as  also  all  other  points,  by  first  finding  their  projections 
as  at  No.  2,  and  the  heights  of  these  points  upon  the  oblique  line  aa,  No. 
3,  and  then  transferring  the  points  thus  found  upon  the  perpendicular  AT. 
Through  the  points  found  in  the  perpendicular  at,  draw  lines  parallel  to  uv,  to 
intersect  with  lines  drawn  perpendicular  to  uv  from  the  projections  of  the  points 
to  be  found  in  No.  2,  and  the  points  of  intersection  of  every  two  lines  will  be 
the  points  in  the  oblique  face  of  the  arch,  corresponding  to  those  in  the  section, 
No.  1 

The  curve  thus  found  in  the  oblique  face  of  the  arch  will  be  an  oblique  curve  ; 
therefore  the  line  uv  will  not  be  an  axis,  but  a  diameter. 


ON  OBLIQUE  ARCHES. 


To  find  the  direction  of  any  joint  in  the  oblique  face  of  the  arch, 
the  plane  of  the  joint  being  perpendicular  to  the  springing  plane  of 
the  arch. 

Suppose,  for  instance,  the  plane  passing  through  LT  in  the  elevation,  No.  1} 
perpendicular  to  UV.  Find  the  projection  t  and  I  in  the  horizontal  plane  of  pro- 
jection of  the  points  repiesented  by  T  and  L  in  the  vertical  plane  of  projection* 
and  find  the  point  i  in  the  curve  of  the  oblique  face  of  the  arch,  corresponding 
to  the  point  T  in  the  vertical  plane  of  projection  ;  then  joining  the  points  I  and  i, 
the  straight  line  li  will  be  the  position  of  the  joint  in  a  plane  perpendicular  to 
the  springing  plane  of  the  intrados  of  the  arch. 

PROBLEM  III. 

To  construct  an  oblique  arch  for  a  canal  with  a  cylindric  intrados, 
so  that  the  sides  of  the  coursing  joints  may  be  in  planes  which  inter- 
sect each  other  in  straight  lines  perpendicular  to  the  two  faces  of 
the  arch,  and  parallel  to  the  horizon,  and  that  the  planes  of  the 
coursing  joints  may  make  equal  angles  with  each  other  : — 

Plate  IX.  Jig.  1.  Let  ABCD  be  the  plane  of  the  arch  ;  AD  and  BC  being  the 
planes  of  the  faces,  and  AB,  DC,  the  plans  of  the  springing  lines  of  the  intrados 
of  the  arch  parallel  to  the  line  of  direction  of  the  canal. 

Find  the  middle  point  e  of  the  parallelogram  ABCD,  and  draw  ef  perpendicu- 
lar to  AD  or  BC.  Through  any  convenient  point  fine/  draw  GH  perpendicular 
to  ef,  and  from  the  point  /  with  a  radius  equal  to  half  of  AD  or  BC,  describe  the 
semi-circumference  ikl  meeting  GH  in  i  and  I.  Divide  the  circumference  ikl 
from  i  into  as  many  equal  parts  as  the  coursing  joints  are  intended  to  be  in 
number:  for  example,  let  it  be  divided  into  nine  equal  parts,  ij,  12,  23,  &c. 
Draw  the  tangent  QR  parallel  to  GH,  and  from  f}  and  through  the  points  1,  2, 
3,  &c.  of  division,  draw  the  straight  lines,  fm,fn,fo,fp,  &c.  meeting  QR  in  the 
points  m,  n,  o,  p. 

Through  e  draw  st  parallel  to  AB  or  DC,  and  draw  ms,  nu,  ow,  py,  perpendicu- 
lar to  GH,  meeting  st  in  the  points  s,  u,  w,  y.  Make  ez,  ex,  ev,  et,  equal  respect- 
ively to  ey,  ew,  eu,  et.  Prolong  CD  to  meet  ef  in  y,  and  prolong/e  and  AB  to 
meet  each  other  in  the  point  @ ;  then  with  the  two  diameters  st  and  0y  describe 
the  ellipse  sfity,  and  with  the  two  diameters  uv  and  fiy  describe  the  ellipse 
ugvy,  and  so  on  ;  then  the  portions  of  these  curves  comprised  between  the  lines 
AD  and  BC,  will  be  the  plans  of  the  coursing  joints. 

The  method  which  has  now  been  shown  for  finding  the  joint  lines  of  the  in- 
trados of  the  arch  is  quite  satisfactory  as  to  the  principle,  since  it  exhibits  the 
plans  of  the  complete  sections  of  the  cylinder  by  the  cutting  planes  of  the  joints 
to  the  several  angles  of  inclination.  We  shall  show  how  the  joint  lines  of  the 
intrados  themselves  may  be  found,  as  depending-  upon  the  plans  of  the  joints. 

To  find  the  plane  curves  for  the  joints  of  the  intrados  : 

Having  found  the  conjugate  diameter  0y,  and  the  semi-conjugate  es,  as  also 
the  semi-conjugate  diameter  eu,  eiv,  ey,  Plate  IX.fg.S,  as  has  been  shown  in  the 
immediately  preceding  plate,  proceed  in  the  following  manner.  Draw  st,  uv,  ivx, 
yz,  perpendicular  to  es,  and  make  st,  uv,  wx,  yz,  each  equal  to  the  radius  of  the 
gemi-circle  ikl.    Join  et,  ev,  ex,  ez.    Draw  ss',  uu',  ww',  yy',  perpendicular  to  fiy  or 


94  OPERATIVE  MASONRY. 


/?/*;  and  from  the  point  c  as  a  centre,  with  the  radii  et,  ev,  ex,  ez,  describe  the  arcs 
is',  vu't  xw',  zy'.    Join  es',  eu',  ew',  ey'. 

With  the  diameters  es',  eu',  ew',  ey',  and  with  their  common  conjugate  (ty,  de- 
scribe the  semi-ellipsis  @s'y,  fiu'y,  ftw'y,  j2y'y,_&LC.  then  the  portions  of  these  curves 
contained  between  the  lines  BC  and  AD  will  be  the  curve  lines  of  the  joints 
required. 

Let  ABCD,  jig.  2,  be  the  plan,  which  is  a  parallelogram  as  before.  Divide  AB 
into  any  number  of  equal  parts,  as,  for  example,  into  four,  at  the  points  1,  2,  3, 
and  draw  the  lines  la,  2/2,  Sy,  parallel  to  BC  or  AD,  meeting  DC  in  the  points 
a,  @,  y,  and  let  hg  be  the  ground-line  of  the  elevation  ;  then  AD,  la,  2/?,  Sy,  BC, 
are  the  plans  of  semi-circular  sections  of  the  intrados,  and  are  each  parallel  to 
the  ground-line  hg,  the  elevations  of  these  plans  will  be  semi-circles. 

These  elevations  being  described,  let  efg  be  the  elevation  to  the  plan  BC,  klm 
the  elevation  to  the  plan  2/2  in  the  middle,  between  the  plans  BC  and  AD  of  the 
semi-circular  sections  of  the  cylinder.  Let  c  be  the  centre  of  the  semi-circular 
arc  klm,  and  divide  the  semi-circular  arc  klm  into  as  many  equal  parts  as  there 
are  intended  to  be  courses  in  the  arch  ;  for  example,  let  the  number  of  courses 
be  nine,  and  therefore  the  semi-circular  arc  klm  must  be  divided  into  nine  equal 
parts,  in  the  points  1,  2,  3,  &c. 

From  the  centre  c,  &c.  and  through  the  points  of  division  1,  2,  3ydraw  lines 
which  will  be  the  elevation  of  the  joints,  and  let  pt  be  one  of  these  lines,  inter- 
secting the  five  semi-circles  in  the  points^?,  q,  r,  s,  t.  Draw  the  lines pu,  qv,  rw, 
sx,  ty,  perpendicular  to  the  ground-line  hg,  intersecting  the  plans  AD,  la,  20,Sy, 
BC,  in  the  points  u,  v,  w,  x,  y,  and  the  line  uvwxy  being  drawn,  will  be  the  cor- 
rect plan  of  the  joint  required. 

In  the  same  manner  the  plans  of  the  remaining  joints  may  be  found. 

Let  lad  Jig.  4,  be  the  plan  of  one  pier,  and  ycf  the  plan  of  the  other  pier,  ad 
and  cf  being  the  plans  or  horizontal  sections  of  the  springing  lines  of  the  in- 
trados ;  also,  let  LF  be  the  ground-line  parallel  to  the  planes  of  the  front  and 
rear  elevations.  Describe  the  five  semi-circles  in  the  elevation  as  before,  ABC 
being  that  in  the  front,  DEF  that  in  the  rear,  and  GH1  that  belonging  to  the 
middle  section. 

Divide  the  semi-circular  arc  GHI  into  the  number  of  equal  parts  required,  and 
let  the  points  of  division  be  1,2,  3,  &c.  Through  the  points  1,  2,  3,  &c.  draw 
the  straight  lines  lo,  25,  3U,  &c.  radiating  to  the  centre  of  the  semi-circular  arc 
ABC'  intersecting  the  curve  ABC  in  the  points  N,  R,  T,  and  the  lines  NO,  RS, 
TU,  will  be  the  joint  lines  of  the  face,  and  will  be  perpendicular  to  the  curve 
line  ABC. 

In  the  straight  line  ac,  which  is  the  plan  of  the  face  of  the  arc,  take  a  part  in 
for  the  joint  in  the  direction  NO  of  the  elevation,  and  let  the  lines  IN,  2R,  3T, 
intersect  the  semi-circular  arc  between  the  parallel  sections  ABC  and  DEF  in 
the  points  a,  @,  y,  &c.  Let  the  points  u  and  v  be  in  the  straight  line  ac.  Make 
nu  and  uv  respectively  equal  to  Na,  a  I,  and  draw  uw  and  vx  perpendicular  to  zv. 

Divide  ad  into  as  many  equal  parts  as  the  thickness  of  the  arch  is  divided  into 
equal  parts  by  the  planes  of  the  semi-circular  arcs  which  are  parallel  to  the 
planes  of  the  front  and  rear  faces  ;  that  is,  divide  ad  into  four  equal  parts,  and  let 
ak,  ag,  be  two  of  those  parts  in  succession,  and  draw  kw  and  gx  parallel  to  ac ; 
then,  n,  w,  x,  will  be  three  points  in  the  curve,  which  is  the  intersection  of  the 
plane  of  the  curving  joint  and  the  cylindric  surface  forming  the  intrados ;  and 


AJHLCfflt  WITH  &:PXTLflJL  , 


PL  /: 


ON  OBLIQUE  ARCHES. 


95 


thus  we  might  find  as  many  points  as  we  please,  by  increasing  the  number  of 
equi-distant  sections.  This  gives  the  first  joint  next  in  succession  to  the  spring- 
ing AD. 

In  the  same  manner  all  the  other  coursing  joints  will  be  found  as  at  No.  2,  No. 
3,  No.  4,  &c. 

Observations  on  the  preceding  methods  : — 

The  most  simple  construction  of  an  oblique  arch  with  a  cylindrical  intrados,  is 
that  where  the  sides  of  the  coursing  joint  are  in  plane  intersecting  the  intrados 
perpendicularly  in  straight  lines,  as  in  the  first  example  ;  but  when  the  arch  is 
very  oblique,  the  coursing  joints  intersect  the  planes  of  the  two  vertical  faces  ill 
very  oblique  angles. 

It  has  been  shown  that  when  the  sides  of  the  coursing  joints  are  in  planes 
perpendicular  to  the  front  and  rear  faces,  these  planes  cut  the  intrados  very 
obliquely,  except  at  the  middle  section,  or  in  the  best  method  in  the  curve  of  the 
front  and  rear.  It  therefore  appears,  that  in  an  oblique  arch,  in  order  that  the 
surfaces  of  the  coursing  joints  may  intersect  both  the  intrados,  and  the  face  of 
the  arch  perpendicularly,  the  sides  of  the  coursing  joints  cannot  be  in  planes. 

In  order  that  every  arr.h  may  be  the  strongest  possible,  a  straight  line  passing 
through  any  point  of  the  surface  of  a  joint  perpendicularly  to  the  intrados,  ought 
to  have  all  its  intermediate  points  between  the  point  through  which  it  passes, 
and  the  intrados,  in  the  surface  of  the  side  of  the  coursing  joint ;  and  in  order 
that  the  stones  may  be  reduced  to  their  form  in  the  easiest  manner  possible, 
the  surfaces  should  be  uniform  ;  and  the  forms  of  the  stones  should  be  similar 
solids,  and  the  solids  similarly  situated. 

To  obtain  these  desirable  objects  will  not  be  possible  where  the  faces  of  the 
arch  are  plane  surfaces ;  however,  even  in  this  case,  the  joints  may  be  so 
formed  by  uniform  helical  surfaces,  that  they  will  intersect  the  intrados  per- 
pendicularly in  every  point,  and  the  faces  of  the  arch  perpendicularly  in  two 
points  of  the  curve. 

This  mode  of  executing  a  bridge  renders  the  construction  much  stronger 
than  when  the  joints  of  it  are  parallel  to  the  horizon.  Since  in  this  last 
case,  the  angles  of  the  beds  and  the  faces  are  so  acute  upon  one  side,  that 
the  points  of  the  ring-stones  are  very  liable  to  be  broken,  or  eveji  to  be  fractur- 
ed in  large  masses. 

For,  though  the  gravitating  force  acts  perpendicularly  to  the  horizon ;  yet, 
notwithstanding,  when  one  body  presses  upon  the  surface  of  another,  the  faces 
act  upon  each  other  in  straight  lines  perpendicularly  to  their  surfaces.  Hence 
a  right-angled  solid  will  resist  equally  upon  all  points  of  its  surface. 

From  this  consideration,  we  are  induced  to  give  a  preference  to  the  con- 
struction with  spiral  joints,  though  attended  with  greater  difficulty  in  the 
execution. 

PROBLEM  IV. 

To  execute  a  bridge  upon  an  oblique  plan,  with  spiral  joints  rising 
nearly  perpendicular  to  the  plane  of  the  sides. 

Fig.  1,  Plate  XII.,  is  the  plan  of  a  bevel  bridge  ;  Jig.  2,  the  elevation  of  the 
same,  as  the  two  faces  of  the  obtuse  angle  are  shown  ;  the  joints  of  the  intrados 
descend  from  the  face  of  the  arch  in  such  a  manner,  that  supposing  the  lines  ab 
13 


96 


OPERATIVE  MASONRY. 


joints  ba,  b'  a\  b"  a'\  &c.  are  as  nearly  perpendicular  to  the  curve  bbV'b'"  as  pos- 
sible for  the  construction  to  admit  of,  supposing  the  joints  to  be  all  parallel  to 
each  other.  By  making  the  joints  of  the  intrados  all  parallel  to  each  other,  all 
the  intermediate  arch-stones  will  have  the  same  section  when  cut  by  a  plane  at 
right  angles  to  the  arris-line  of  the  bed  and  intrados  of  the  arch ;  therefore,  if 
the  intermediate  arch-stones  are  equal  in  length,  the  upper  and  lower  beds  must 
be  the  same  winding  surfaces,  and  consequently  must  all  coincide  with  each 
other,  and  all  the  end-joints  must  be  equal  and  similar  surfaces,  and  thus  all  the 
arch-stones  may  be  equal  and  similar  bodies. 

The  most  considerable  obliquity  of  the  joints  in  the  intrados  is  at  those  two 
parts  of  the  curve  where  it  meets  the  horizon.  The  obliquity  of  the  intradosal 
joints,  at  the  crown  of  the  arch,is  considerably  less  than  at  the  horizon  ;  but  in 
the  middle  of  that  portion  of  the  curve,  between  the  crown  and  the  horizon  on 
each  side,  the  intradosal  joints  are  exactly  perpendicular  to  the  horizon. 

Had  it  not  been  for  these  deviations,  the  execution  of  this  arch  would  have 
been  extremely  easy,  and  very  few  constructive  lines  would  have  been  necessary. 

This  arch,  however,  might  be  executed  so  that  all  the  intradosal  joints  would 
be  perpendicular  to  the  curve-line  of  the  face  and  intrados ;  but  this  position 
would  have  caused  such  a  diversity  in  the  form  of  the  stones  as  to  increase  the 
labor  in  a  very  great  degree,  and,  consequently,  to  render  the  execution  very  ex- 
pensive ;  and  not  only  so,  but  as  the  joints  would  have  been  out  of  a  parallel, 
their  effect  would  have  been  very  unsightly.  A  succession  of  equal  figures,  simi- 
larly formed,  has  a  most  imposing  effect  on  the  eye  of  the  spectator.  The  laws 
of  perspective  produce  on  the  imagination  a  most  fascinating  variety,  the  figure 
only  varying  by  imperceptible  degrees,  which  yet  in  the  remote  parts  produces 
a  great  change. 

There  is  still  another  method  in  which  the  greater  part  of  the  difficulty  may 
be  removed  without  impairing  the  strength  of  the  arch ;  this  manner  is  to  form 
the  ring-stones  so  that  the  joints  in  the  intrados  may  be  perpendicular  to  the 
curve  forming  its  edge ;  the  intermediate  portion  of  the  intrados  to  be  filled  in 
with  arch-stones,  which  have  their  soffit-joints  parallel  to  the  horizon.  This 
disposition  of  the  joints  might  not  be  so  pleasant  to  the  eye,  but,  if  well  executed, 
it  could  not  be  disagreeable. 

If  the  ends  were  made  to  form  spirals,  as  in  f  g.  3,  and  a  wall  erected  above 
the  arch,  as  this  wall  could  only  be  made  to  coincide  in  three  points  at  most 
with  the  face  of  the  arch,  no  regular  form  of  work  could  be  introduced  so  as  to 
connect  the  wall  to  the  ring-stones. 

To  form  the  developement  of  the  intrados  of  the  oblique  arch, 
with  spiral  or  winding  joints,  and  thence  to  find  the  plan  of  the  de- 
velopement or  intrados. 

Let  AC,  Plate  XIII.,  be  the  inner  diameter  of  the  face  of  the  ring-stones  ; 
upon  AC  describe  the  semi-circular  arc  ABC,  and  find  its  developement  upon 
the  straight  line  AD.    Draw  the  straight  lines  AG  and  DI  perpendicular  to  AD. 

In  AG  take  any  point  M,  and  draw  ML,  making  the  angle  AML  equal  to  the 
angle  of  the  bevel  of  the  bridge,  meeting  CH  in  the  point  L.  Draw  La  perpen- 
dicular to  AG',  meeting  AG  in  a.    Prolong  La  to  meet  DI  in  Q,  and  draw  ON 


M  YWLbFWt  ENT  QflF  '1  II  S  I  KTB  AIM  i§ 


77.  7J. 


ON  OBLIQUE  ARCHES. 


97 


section  of  the  face  of  the  arch  and  intrados  in  the  points  &',  b',  b' ,  &c.  then  the 
a'b',  a"b'',  Jig.  1,  to  be  the  joints  of  the  intrados,  meeting  the  curve  of  the  inter- 
parallel  to  LM,  so  that  the  distance  between  LM  and  ON  may  comprise  the 
breadth  of  the  bridge.  Let  ON  meet  CH  in  O,  and  AG  in  N ;  then  will  LMNO 
be  the  plan  of  the  bridge.  Find  the  developement  MPQSRN  upon  the  straight 
line  AG',  the  curve  MPQ  being  the  developement  of  the  arc  insisting  on  ML, 
and  NRS  the  developement  of  the  curve  line  upon  NO. 

Draw  MQ,  and  divide  MQ  into  as  many  equal  parts  as  there  are  intended 
to  be  arch-stones,  which  we  shall  here  suppose  to  be  fifteen ;  hence  there 
will  be  a  ring-stone  in  the  middle,  and  the  number  of  ring-stones  will  be 
equal  on  each  side  of  the  middle  one ;  let  P  be  the  middle  point  of  the  line 
MQ,,  and  let  a,  6,  c,  &c.  be  the  points  of  division  on  one  side  of  P,  and  a,  b,  c, 
&c.  the  points  of  division  on  the  other  side. 

Through  the  middle  point  P  draw  the  straight  line  WX.  Through  the 
points  a,  6,  c,  &c.  draw  the  lines  c?o,  ep,fq,  &c.  parallel  to  WX,  meeting  the 
curve  MQ,  in  the  points  k}  Z,  m,  &c.  and  the  curve  NS  in  the  points  o,  p,  q, 
&c;  also  through  the  points  a',  b\  c',  &c.  draw  the  lines  rfV,  e'f,  p'q\  &c. 
parallel  to  WX,  meeting  the  curve  MQ  in  the  points  k\  V,  m',  &c,  and  the 
curve  NS  in  the  points  o',  p\  q',  &c. ;  then  ao,  lp,  mq,  &c. ;  also  do',  lp',  m'q", 
&c.  will  be  the  joint  lines  on  the  intrados  of  the  arch;  the  heading  joints  are 
marked  on  the  developement  at  right  angles  to  these  joints. 

Now  as  all  the  intermediate  arch-stones  are  equal  and  similar,  it  will  only  be 
necessary  to  show  how  one  of  the  stones  may  be  formed.  For  this  purpose,  let 
uvwx  be  the  developement  of  the  soffit.  Draw  vy  parallel  to  MN  or  QS.  Run  a 
straight  draught  vy  diagonally  upon  the  intrados  of  the  stone,  making  an  angle 
uyv  with  the  edge  uy,  or  ux,  of  the  soffit.    Draw  ua  and  w°-  perpendicular  to  vy. 

Make  two  moulds  Z,Z  to  the  arc  ABC,  so  that  their  chords  may  be  equal ; 
then  cut  two  draughts  ua  and  no  so  as  to  coincide  with  the  convex  edges  of  the 
two  moulds  Z,Z,  while  the  straight  edges  of  the  two  moulds  Z,Z  are  out  of 
winding. 

That  is,  apply  the  moulds  Z,Z  at  the  same  time ;  the  one  upon  the  line  ua 
and  the  other  upon  the  line  nv,  and  sink  a  cavity  or  draught  under  each  line ; 
so  that,  after  one  or  more  trials,  the  convex  edge  may  coincide  with  the  bottom 
of  each  draught ;  and  that  the  point  marked  upon  each  circular  edge  may  coin- 
cide with  the  bottom  of  the  draught  vy ;  and  that  the  two  chord-lines  of  each 
circular  mould  may  be  in  the  same  plane,  that  is,  in  workman's  terms,  out  of 
winding  or  out  of  twist. 

The  remaining  superfluous  part  may  be  worked  off  as  directed  by  two 
straight  edges,  and  thus  the  cylindric  surface  of  the  soffit  of  the  fctone  will  be 
formed. 

The  longitudinal  spiral  joints  may  be  formed  by  means  of  the  bevel  atr,  where 
it  is  applied  to  the  section  of  one  of  the  arch-stones :  but  before  the  heading 
joints  and  beds  are  wrought,  a  pliable  or  flexible  mould  uvwx  must  be  made,  and 
bent  to  the  convexity  of  the  surface,  so  that  the  line  vy  may  coincide  with  the 
bottom  of  the  straight  draught  first  wrought. 

In  applying  the  mould  r,  the  curve  edge  must  be  laid  along  the  line  ua  or  iw ; 
and  in  directions  parallel  to  these  lines;  and  several  draughts  must  be  wrought 
in  the  spiral  bed,  so  as  to  coincide  with  the  straight  edge,  and  the  angular  with 
the  line  vw,  or  ux. 


98 


OPERATIVE  MASONRY. 


Having  shown  the  developement  of  the  intrados  and  its  projection, 
it  will  be  proper  to  show  how  the  curves  are  projected. 

Let  the  line  AF,  Plate  XIV,  the  edge  of  the  triangle  AEF,  be  the  developement 
of  one  of  the  longitudinal  joints,  and  letHG  at  right  angles  to  AF  be  the  develope- 
ment of  one  of  the  lines  of  direction  of  the  heading  joints  ;  then,  as  the  projec- 
tion of  all  the  longitudinal  lines  is  equal  and  similar,  and  the  projection  of  the 
heading  joints  is  equal  and  similar,  one  curve  of  each  being  obtained,  and  a 
mould  formed  thereto,  each  series  of  curves  may  be  drawn  by  means  of  its 
proper  mould. 

Divide  the  arc  ABC  into  any  number  of  equal  parts  at  the  points  1,  2,  3,  &c. 
and  the  straight  line  AF  into  the  same  number  of  equal  parts  at  the  points  1,2,3, 
&c. ;  but  it  will  be  most  convenient  to  divide  each  into  as  many  equal  parts  as 
the  ring-stones  are  in  number,  which  in  this  example  are  fifteen.  From  the 
points  1,  2,  3,  &c.  of  division  in  the  straight  line  AF,  draw  la,  2b,  3c,  &c.  per- 
pendicular to  AE,  and  through  the  points  1,  2,  3,  &c.  in  the  arc  CB,  draw  lines 
la,  2b,  3c,  &c,  parallel  to  CD,  and  through  the  points  a,  b,  c,  &c.  draw  a  curve, 
which  is  the  projection  of  a  cylindric  spiral,  and  is  the  plan  of  one  of  the  longi- 
tudinal joints  required.  In  the  same  manner,  dividing  HG  into  the  same  num- 
ber of  equal  parts  as  the  arc  ABC,  and  drawing  lines  as  before  from  the  divisions 
of  the  arc,  and  from  the  divisions  of  the  straight  line  HG,  to  intersect  each  other 
respectively  in  the  points  a,  b,  c,  &c.  we  shall  have  the  curve  of  direction  of  the 
heading  joints.  In  order  to  find  the  direction  of  the  curve  in  the  middle,  it  will 
be  necessary  to  show  the  manner  of  finding  a  tangent  in  the  middle  of  the  curve. 
For  this  purpose, 

Make  the  angle  EAk,  equal  to  EAF,  and  let  the  point  m  be  the  middle  of  the 
curve  DmA.  Through  the  point  m  draw  pg  parallel  to  kA,  and  pg  will  be  the 
tangent  required. 

In  like  manner3  make  the  angle  AH/*  equal  to  AHG,  and  let  g  be  the  middle 
point  of  the  curve  Hg-C ;  through  g  draw  rs  parallel  to  H/J  and  rs  will  be  a  tan- 
gent to  the  curve  Hg-C. 

It  is  here  evident  from  the  tangents,  that  if  these  two  curves  had  intersected 
each  other  in  the  middle,  they  would  have  been  at  right  angles  to  each  other ; 
they  are,  however,  still  the  projections  of  two  straight  lines  bent  upon  the  cylin- 
dric surface. 

To  draw  a  tangent  to  the  point  n.  Draw  n4  parallel  to  EA,  meeting  the 
curve  AB  in  4.  Draw  4u  perpendicular  to  the  radical  line,  and  make  4u  equal 
to  the  developement  of  the  arc  4A.  Draw  ut  perpendicular  to  AG,  and  join  tnf 
which  is  the  tangent  required. 

To  find  the  curvature  of  a  stone  along  the  two  edges  of  the  longi- 
tudinal joints,  and  along  the  heading  joints  of  the  intrados.  In  fig. 
1,  Plate  XV,  which  is  a  developement  of  the  intrados,  abed  is  the 
developement  of  the  intrados  of  an  arch-stone,  it  is  required  to  find 
the  curvature  along  6c,  and  ad,  also  in  the  direction  a&,  dc  at  the 
ends. 

In  Jig.  2,  make  OA  equal  to  the  radius  of  the  cylinder,  and  through  A  draw 
BE  perpendicular  to  AO.  Make  the  angle  BOA  equal  to  the  complement  of 
the  angle  with  the  joints  in  the  developement  of  the  intrados  made  with  the 
springing  lines,  that  is  equal  to  the  angle  DAE,  Jig.  1.    Make  OC,  Jig.  2,  equal 


TO  TIED)  TffiCE  JOINTS  OF  ..  11.15. 


ON  OBLIQUE  ARCHES. 


<)9 


to  OB,  and  draw  OD  perpendicular  to  BC.  Make  OD  equal  to  OA.  Then  with 
the  transverse  axis  BC,  and  semi-conjugate  OD,  describe  the  semi-elliptic  arc 
or  curve  CDB ;  then  the  portion  of  the  elliptic  arc  on  each  side  of  the  point  D 
will  be  the  curvature  in  Jig,  1,  along  the  longitudinal  edge  be  or  da  of  the  soffit 
of  a  stone. 

Again,  produce  DO  to  E,  and  made  OE  equal  to  OD.  In  OB,  take  OG,  equal 
to  OA,  the  radius  of  the  circular  end  of  the  cylinder;  then  with  the  transverse 
axis  DE,  and  the  semi-conjugate  OG,  describe  the  semi-elliptic  arc  DGE,  and 
the  small  portion  of  this  arc  on  each  side  of  the  point  G  has  the  same  curvature 
as  ab  or  dc,  Jig.  1.  Therefore,  the  stone  being  wrought  hollow,  as  directed  in  the 
description  of  the  preceding  plate,  then  the  mould  shown  at  D  is  that  for  work- 
ing the  longitudinal  joints,  or  those  which  terminate  on  the  soffit  in  the  lines  ad 
and  be.  In  like  manner,  the  mould  G  is  that  for  working  the  heading  joints 
which  terminate  upon  the  soffit  in  the  lines  ab,  dc,  &c.  It  will  hardly  be  neces- 
sary to  remind  the  reader,  that  the  convex  edge  of  the  squares  at  D  and  G  is  to 
be  applied  upon  the  hollow  soffit  already  wrought.  The  curvature  of  these 
moulds  may  be  shown  by  calculation  thus:  let  R  be  the  radius  of  curvature, 
a  ssa  the  semi-transverse  axis,  and  b  =  the  semi-conjugate  ;  then  6  :  a  : :  a  : 
a2 

R  =  — . 
b 

As  for  example  to  this  formula,  let  the  radius  of  the  cylindric  intrados,  or 
6  =  13  feet,  and  the  semi-transverse  axis,  or  a  =  28  feet 
28 
28 

224 
56 

13)784(60  feet  4  inches  nearly 
78 

4 
12 

To  find  the  angle  of  the  joints  of  the  face  of  the  arch,  and  intra- 
dos of  the  oblique  arch  with  spiral  joints. 

Let  the  semi-circular  arc  ABC,  Fig.  3,  be  a  section  of  the  intrados  at  right 
angles  to  the  axis  of  the  cylinder.  Draw  CD  and  AE  perpendicular  to  the 
diameter  AC.  Draw  AD,  making  an  angle  with  CD,  equal  to  the  inclination 
which  the  plane  of  the  face  of  the  arch  makes  with  the  vertical  plane  which  is 
parallel  to  the  axis  of  the  cylinder,  and  which  passes  through  the  springing  line 
of  the  arch. 

Find  the  edge  D/Xx  of  the  developement  and  face  of  the  arch,  or  draw  the 
curve  D/G  with  a  mould  made  from  the  developement  before  shown.  Draw  the 
face  of  the  ring-stones  AKD.  Let  it  now  be  required  to  find  the  fourth  from 
the  point  D.  Make  Df  equal  to  the  portion  D4  of  the  intrados  AKD.  Draw// 
the  developement  of  a  part  of  the  longitudinal  spiral  joint  corresponding  to  the 
point  4  of  the  elliptic  arc  AKD.  Draw  the  line  d  a  tangent  to  the  curve  at/. 
To  do  this,  we  shall  a^ain  repeat  the  process  of  which  the  principle  has  already 


I 


100  OPERATIVE  MASONRY. 

been  taught,  viz.  On  CD,  as  a  diameter,  describe  the  semi-circle  CqD,  and 
draw  fq,  intersecting  CD  perpendicularly.  Draw  qu  a  tangent  to  the  semi-circu- 
lar arc  at  the  point  q,  and  make  qu  equal  to  the  developement  of  the  portion  qD 
of  the  semi-circular  arc.  Drawn*  perpendicular  to  CD,  meeting  CD,  or  CD 
produced  in  the  point  t.  Through  /  draw  the  straight  line  U,  and  U  will  be  a 
tangent  to  the  curve  at  the  point.  By  this  means  we  have  the  angles  which  the 
spiral  joints  in  the  intrados  make  at  the  point  4  with  the  elliptic  curve  AKD. 

To  find  the  angle  made  by  the  normal  and  the  curve,  in  fig.  4. 

In  fig.  4,  draw  the  straight  line  ab,  and  make  ab  equal  to  the  radius  of  curva- 
ture of  the  elliptic  arc  AKD  at  the  point  4.  This  radius  would  be  near  enough 
to  make  it  the  half  of  the  half  sum  of  the  semi-parameters  of  the  two  axes. 

But  if  greater  nicety  is  required,  let  the  radius  of  curvature  be  denoted  by  n, 
the  semi-transverse  axis  OD  or  OA  be  denoted  by  a,  and  the  semi-conjugate, 
which  is  the  radius  of  the  semi-circular  arc  ABC,  be  denoted  by  b,  and  let  the  dis- 

tance  Op  be  denoted  by  x;  then  will  r=  1   >    which  will  be  exact 

C  a4&  ) 

to  the  number  of  figures  found  in  the  operation  here  indicated. 

Having  thus  found  the  radius  of  curvature,  either  mechanically  or  by  calcula- 
tion, make  ah,  Jig.  4,  equal  to  that  radius.  From  the  point  a  as  a  centre,  with 
the  distance  ab,  describe  the  arc  be ;  and  draw  the  straight  line  bd  a  tangent  to 
the  curve. 

To  find  the  angle  made  by  a  tangent  plane  to  the  cylindric  surface 
at  the  point  4,  fig.  3,  and  the  plane  of  the  face  of  the  arch. 

Draw  the  straight  line  4n  a  tangent  to  the  elliptic  curve  AKD  at  the  point  4, 
and  draw  4v  parallel  to  AD.    Trasnsfer  the  angle  uiv  to  abc,  Jig.  5. 

In  Jig.  5,  at  the  point  6,  in  the  straight  line  be,  make  the  angle  cbd  equal  to  the 
angle  DOP,  Jig.  3,  which  the  axis  makes  with  the  plane  of  the  face  of  the  arch . 
Again  in  Jig.  5,  draw  cf  perpendicular  to  ab,  intersecting-  ab  in  the  point  a.  Draw 
cd  perpendicular  to  cb,  and  ce  perpendicular  to  cf.  Make  cc  equal  to  cd,  and  join 
ea;  then  will  the  angle  eaf  be  the  inclination  of  the  curved  surface  of  the  cylin- 
dric intrados,  and  the  face  of  the  ring-stones. 

We  have  now  ascertained  two  sides,  and  the  contained  angle  of  the  trehedral  ; 
in  order  to  find  the  remaining  parts,  the  third  side  of  this  trehedral  is  the  angle 
of  the  joints  of  the  intrados  and  face  of  the  arch,  by  applying  the  proper  curved 
moulds  to  the  angular  point ;  it  is,  however,  rather  unfavorable  to  our  purpose, 
that  the  angle  abd,Jig.  4,  is  a  right  angle,  and  that  the  angles  [ft  and  If,  Jig.  3, 
differ  but  in  a  very  small  degree  from  right  angles.  As  from  this  circumstance 
the  principle  cannot  be  made  evident,  we  shall  therefore  suppose,  that  these  an- 
gles have  at  least  a  certain  degree  of  obliquity. 

In  Jigs.  6  and  5,  let  ABC  equal  to  angle  Ift  Jig.  3,  and  ABD,  Jigs.  6  and  7,  equal 
to  the  angle  abd,  Jig.  4:  thus,  in  Jigs.  6  and  7,  draw  De,  intersecting  AB  in  or 
producing  De  to  meet  AB  in  /.  At  the  point  f  in  the  straight  line  ef  in  Jig.  7, 
make  the  angle  efg  equal  to  the  angle  eac,  Jig.  5  ;  or  in  Jig.  6,  make  the  angle 
efg  equal  to  the  supplement  of  the  angle  eaf.  In  figs.  6  and  7,  draw  ek  per- 
pendicular to  BC,  BC  in  i,  or  BC  produced  in  i.  Draw  eg  perpendicular  to 
ef  and  eh  to  eC.  Make  eh  equal  to  eg,  and  join  hi.  Make  iK  equal  to  %h9 
and  join  BK ;  then  will  the  angle  CBK  be  the  angle  of  the  joints  of  the  in- 
trados and  face  of  the  arch. 


ami  iw  a  emcnuiiAx  wasjl  , 


ON  OBLIQUE  ARCHES. 


101 


When  eacli  of  the  given  sides  is  a  right  angle,  then  the  remaining  side  of 
the  trehedral  will  be  the  same  as  the  contained  angle  ;  that  is,  the  angle  of 
the  joints  .of  the  intrados  and  face  of  the  arch,  will  be  the  same  as  the  angle 
eaf,  Jig.  5.  In  this  case,  no  lines  are  necessary  in  order  to  discover  the  an- 
gle of  the  joints. 

In  order  to  apply  the  angle  CBK,  one  of  the  lines  which  applies  to  the 
face  must  be  straight,  and  the  curved  edge  shown  by  the  bevel  at  D  of  the 
preceding  plate  must  be  so  applied,  that  the  other  leg  of  the  bevel  may  be 
a  tangent  to  the  curve  at  the  angular  point  B,  and  this  will  complete  what 
is  necessary  in  the  construction  of  an  oblique  arch  with  spiral  joints. 


SECTION  VII. 
A  CIRCULAR  ARCH  IN  A  CIRCULAR  WALL. 
PROBLEM  I. 

To  execute  a  semi-cylindric  arch  in  a  cylindric  wall,  supposing 
the  axes  of  the  two  cylinders  to  intersect  each  other.  Given  the  two 
diameters  of  the  wall,  and  the  diameter  of  the  cylindric  arch,  and 
the  number  of  arch-stones. 

Fig.  1,  Plate  XVI.  From  any  point  o  with  the  radius  of  the  inner  circle  of 
the  wall  describe  the  circle  ABC,  or  as  much  of  it  as  may  be  necessary  ;  and 
from  the  same  point  o,  with  the  radius  of  the  exterior  face  of  the  wall  describe 
the  circle  DEF,  or  as  much  of  it  as  may  be  found  convenient. 

Apply  the  chord  AB  equal  to  the  width  of  the  arch,  and  draw  DA  and  EB 
perpendicular  to  AB  or  DE  ;  then  ABDE  will  be  the  plan  of  the  cylindric  arch 

Draw  Op  perpendicular  to  AB,  and  draw  tv  perpendicular  to  Op.  From  the 
point  p  as  a  centre,  with  the  radius  of  the  intrados  of  the  arch  describe  the  semi- 
circular arc,  qrs  ;  and  from  the  same  point  p,  with  the  radius  of  the  extrados,  de- 
scribe the  semi-circular  arc  tuv.  Divide  the  arc  qrs  into  as  many  equal  parts  as 
the  arch-stones  are  intended  to  be  in  number,  that  is,  here  into  nine  equal  parts. 
From  the  centre  p,  draw  lines  through  the  points  of  division  to  meet  the  curve 
tuv  ;  and  these  lines  will  be  the  elevation  of  the  joints  ;  and  the  joints,  together 
with  the  intradosal  and  extradosal  arcs,  will  complete  the  elevation  of  the  arch. 

Find  the  developement,/g*.  2,  as  in  Jig.  3,  Plate  VIII,  and  the  parallel  equi-distant 
lines  to  the  same  number  as  the  joints  in  the  elevation,  will  be  the  joints  of  the 
soffits  of  the  stones ;  and  the  surfaces  comprehended  by  the  parallel  lines,  and 
the  edges  of  the  developements,  will  be  the  moulds  for  shaping  the  soffits  of  the 
stones. 

In  Jig.  3.  Let  AB  be  equal  to  the  diameter  of  the  external  cylinder.  Draw 
AC  and  BD  each  perpendicular  to  AB.  Bisect  AB  in  p,  from  which  describe 
the  interdosal  and  extradosal  arcs,  and  draw  the  joints  as  in  Jig.  1.  Produce  the 
joints  to  meet  AC  or  BD,  in  the  point  e,  /,  g,  &c. ;  then  it  is  evident  that  since 
•every  section  of  a  cylinder  is  an  ellipse,  the  lines  p  A,  pe,  pf}  pg,  &c.  are  the  semi- 
transverse  axis  of  the  curves,  which  form  the  joints  in  the  face  of  the  arch,  and 
that  these  curves  have  a  common  semi-conjugate  axis  equal  to  half  the  diameter 
of  the  cylinder. 


102 


OPERATIVE  MASONRY. 


Therefore  upon  any  indefinite  straight  line^Q,  fig.  4,  set  off  the  semi-axis  pA, 
pe,  pf,  pg,  &c.  and  draw  pB  perpendicular  to  pQ.  From  p,  with  the  radius  pA, 
describe  an  arc  AB.  On  the  semi-axes  andpB,  describe  the  quadrantal  curve 
of  an  ellipse  ;  in  the  same  manner  describe  the  quadrantal  curves  /B,  gB,  &c. 
Make  pq  equal  to  pq,  Jig.  3,  and  in  Jig.  4  draw  qt  parallel  to  pB,  intersect  the 
curves  AB,  eB,  fB,  &c.  in  the  points  i,  k,  I,  &c. ;  then  him,  hkn,  hlo,  &c.  are  the 
bevels  to  be  applied  in  forming  the  angles  of  the  joints  :  viz.  the  bevel  him  is  that 
of  the  impost,  the  straight  side  hi  being  applied  upon  the  soffit  or  intrados ;  and 
the  curved  part  im  horizontally  to  the  curve  of  the  exterior  side  of  the  wall :  the 
point  k,  of  the  bevil  hkn,  Jig.  4,  applies  to  the  point  k,  Jig.  3,  so  that  kh  may  coin- 
cide with  the  joint  upon  the  intrados,  and  the  curved  edge  kn,  fig.  4,  upon  the 
face  kn,Jig.  3  ;  and  so  on. 

As  to  the  angles  which  the  beds  of  the  stones  make  with  the  intrados,  they 
are  all  equal,  and  may  be  found  from  the  elevation  svyx,  Jig.  1 ;  which  is  the 
same  as  a  section  of  one  of  the  arch-stones  perpendicular  to  any  one  of  th*  joints 
on  the  soffits. 

The  faces  of  the  stones  must  be  wrought  by  a  straight  edge,  by  perpendicular 
lines.  The  first  thing  to  be  done  is  to  work  one  of  the  beds;  secondly,  work 
the  intrados — at  first  as  a  plane  surface  at  an  angle  sxy,  or  xsv,Jig.  1 ;  then  gauge 
off  the  bed  of  the  soffit,  and  work  the  other  bed  of  the  stone  by  the  ang-le  vsx  or 
yxs;  then  apply  the  proper  soffit,  1,  2,  or  3,  fig.%;  and  lastly,  the  two  moulds 
in  Jig.  4. 


SECTION  VIII. 
A  CONIC  ARCH  IN  A  CYLINDRIC  WALL. 
PROBLEM  I. 

To  execute  a  semi-conic  arch  in  a  cylindric  wall,  supposing  the 
vertex  of  the  cone  to  meet  the  axis  of  the  cylinder.  Given  the  in- 
terior and  exterior  diameters  of  the  wall,  the  length  of  the  axis  of 
the  cone,  and  the  diameter  of  its  base. 

EXAMPLE  I. 

From  the  point  o,  Jig.  1.  Plate  XVII,  with  the  radius  of  the  interior  surface  of 
the  wall  describe  the  arc  ABC,  and  from  the  same  point  O  with  the  radius  of  the 
exterior  surface,  describe  the  arc  DEF,  and  the  area  between  the  arcs  ABC 
and  DEF  will  contain  the  plan  of  the  wall. 

Draw  any  line  Op,  and  make  Op  equal  to  the  length  of  the  axis  of  the  cone. 
Through  p  draw  tv  perpendicular  to  Op.  From p  as  a  centre,  with  the  radius 
of  the  base  of  the  cone,  describe  the  semi-circle  qrs  meeting  tv  in  the  points  q  and 
s.  Divide  the  arc  qrs  into  as  many  equal  parts  as  the  arch-stones  are  to  be  in 
number,  that  is,  in  this  example,  into  nine  equal  parts.  Through  the  points  of 
division  draw  the  joint  lines,  which  will  of  course  radiate  from  the  centre  p. 
The  extradosal  line  tuv  is  here  described,  as  we  here  suppose  the  cone  to  be  of 
an  equal  thickness,  and  consequently  the  axis  of  the  exterior  cone  longer  than 
that  of  the  interior. 


ON  OBLIQUE  ARCHES. 


From  the  points  1,  2,  3,  &c.  where  the  lower  ends  of  the  joints  of  the  arch 
stones  meet  the  intradosal  are,  draw  lines  perpendicular  to  tv,  meeting  tv  in  the 
points  i,  k,  I,  m,  &c.  From  these  points  draw  lines  to  the  vertex  of  the  cone  at 
o,  meeting  the  arc  DE  or  plan  of  the  wall  under  the  arch,  in  the  points  a,  b,  c,  d, 
&c.  Draw  the  lines  ae,  bj)  eg,  dh,  &c,  parallel  to  the  chord  DE,  to  meet  op  in 
iv.  In  fig.  2,  draw  the  straight  line  AB,  in  which  take  the  point  p  near  the  mid- 
dle of  it,  and  make  pA,  pB,  each  equal  to  the  radius  of  the  exterior  surface  of  the 
cylindric  wall.    Through  the  points  A  and  B  draw  fg,  fg,  perpendicular  to  AB. 

From  the  point  p  as  a  centre,  with  any  radius,  describe  a  semi-circular  arc,  and 
divide  it  into  nine  equal  parts  as  before.  Through  the  points  of  division  draw 
the  radiating  lines  to  meet  fg  in  the  points  e,  f  g,  &c.  From  Jig.  1  transfer  the 
distances  Ew,  ac,  bfi  eg,  &c.  fig.  1  to  pg,  fig.  2pr,ps,pt,  &c.  on  each  side  of  the  point 
p.  Draw  the  perpendiculars  rk,  si,  tm,  &c.  to  AB,  which  will  intersect  with  the  ra- 
dials  pe,pf,pg,  &c.  in  the  points  k,  I,  m,  &.c. ;  through  the  points  k,l,  m,  &e.  on 
each  side  draw  a  curve,  and  this  curve  will  be  the  elevation  of  the  intrados  of 
the  arch. 

Fig.  3  exhibits  another  method  by  which  the  heights  of  the  points  k,  I,  m,  fig.  2 
might  have  been  found.  This  method  is  as  follows  : — Upon  a  straight  line  ab,  and 
from  the  point  a  make  ab',  ac,  ad,  ae,  &c.  and  of  respectively  equal  to  ox,  ok,  olT 
Sec.  Jig.  1.  In  Jig.  3,  draw  the  straight  lines  bg,  eh,  di,  ek,  fo,  perpendicular  to 
ab.  Make  bg,  eh,  di,  ek,  respectively  equal  to  the  heights  tl,  k2,  13,  mi.  Draw 
the  straight  lines  ag,  ah,  ai,  ak.  intersecting  fo  in  the  points  I,  m,  n,  o. 

In  Jig.  2,  make  rk,  si,  im,  un,  respectively  equal  to  fl,  fm,  fn,  fo,  fig.  2r 
and  thus  the  points  k,  I,  m,  &c.  are  found  by  a  different  method,  which  is  more 
accurate  for  ascertaining  the  points  near  the  top,  as  the  radials  and  the  perpen- 
diculars intersect  more  and  more  obliquely  as  they  approach  the  summit. 

In  some  line  pQ,,fig.  4,  make  pA,  pe,  pfpg,  &c.  equal  to  pA,pe,  pf  pg,  &c.  fig. 
2.  Draw  pB  perpendicular  to  pQ,.  From  p  with  the  radius  pA,  describe  the  arc 
AB.  With  the  several  semi-axes  pe,  pB ;  pf,  pB ;  pg,  pB,  &c.  describe  the 
quadrantal  elliptic  curves  e?iB,  foB,  &c.  Draw  Bu  parallel  to  AQ.  Make  the 
angle  Bpt  equal  to  the  angle  P,  oE,fig.  1 ;  and  let  i,  k,  I,  &c.  be  the  points  where 
pt  intersects  the  curves  AB,  eB,  fB,  &c.  Then  the  be  vels  of  the  joints  are  him, 
hkn,  Mo,  &lc. 

Now,  if  EBCF,  Jig.  1,  be  the  developement  of  the  intrados,  with  the  joints 
drawn  on  it,  we  shall  have  the  soffits  of  the  stones. 

In  fig.  5,  draw  ab  and  ae  at  a  right  angle  with  each  other.  Make  ab  equal  to 
the  radius  of  the  base  of  the  cone,  and  ac  equal  to  the  length  of  its  axis.  Join 
be.  From  a,  with  the  radius  ab,  describe  an  arc,  dbe.  Make  be  equal  to  the 
chord  of  the  intrados  of  one  of  the  arch-stones.  Produce  be  to  any  point  /,  and 
draw^-  perpendicular  to  ab,  meeting  ab  in  g.  Draw  gi  perpendicular  to  be, 
and  gh  parallel  to  be.  Make  gh  equal  to  gf  and  join  hi;  then  hig  is  the  angle 
which  the  soffits  of  the  stones,  when  wrought  as  planes,  make  with  the  beds. 

EXAMPLE  II. 

To  construct  an  arch  in  a  cylindric  wail,  of  which  arch  the  intra- 
dos is  a  uniform  conic  surface,  so  that  the  axes  of  conic  and  cylin- 
dric surfaces  may  meet  or  intersect  each  other. 

14 


104 


OPERATIVE  MASONRY. 


In  jig.  1,  Plate  XVIII,  which  is  the  plan  and  elevation  of  the  arch,  the  ele- 
vation being  above,  and  the  plan  below,  as  usual,  let  AD  be  considered  as  the 
ground-line,  and  ABD  the  elevation  of  the  base  of  the  cone,  which  base  is  sup- 
posed to  be  a  tangent  plane  to  the  surface  of  the  wall ;  let  bd,  parallel  to  the 
ground-line  AD,  be  the  half  plan  of  the  base  of  the  cone ;  a'b'c'hgj  the  plan  of 
the  cylindric  face  of  the  wall;  and  d'rmlk  the  plan  of  the  intersections  of  the 
conic  and  the  intermediate  cylindric  surfaces  which  terminate  the  interior  of 
the  aperture  of  the  arch. 

First,  to  find  the  elevation  of  the  intersections  of  the  cylindric  face  of  the  wall 
and  the  conic  surface  of  the  intrados.  Having  divided  the  semi-circular  arc 
DBA,  into  the  equal  parts  Dl',  1'2',  2'3',  &c.  at  the  points  V,  2\  3',  &c,  draw 
the  connecting  lines  Bd,  1 1,  2'2,  3'3,  &c.  meeting  bd  in  the  points  d,  1,  2,  3,  &c. 
Draw  be  perpendicular  to  bd,  and  make  be  equal  to  the  axis  of  the  conic  surface. 

Draw  the  straight  lines  dc,  lc,  2c,  &c.  meeting  the  plan  of  the  face  of  the 
wall  in  the  points  /,  g,  h,  and  draw  the  connecting  lines  JF,  gG,  7iH,  &c.  inter- 
secting the  lines  FC,  GC,  HC,  &c.  in  the  points  F,  G,  H,  &c.  A  sufficient  num- 
ber of  points  being  found  in  the  same  manner,  through  these  points  draw  the 
curve  EBF,  and  the  curve  EBF  will  be  the  elevation  of  the  line  of  intersection 
of  the  conic  and  cylindrical  surfaces  required. 

To  find  the  elevation  of  the  intersection  of  the  conic  surface  with  the  inter- 
mediate concentric  cylindric  surface.  Let  the  arc  d'rk  be  the  plan  of  this  con- 
centric cylindric  surface,  having  the  same  centre  as  the  arc  a'  b'  f,  which  is  the 
plan  of  the  cylindric  surface  of  the  wall ;  and  let  the  straight  lines  dc,  lc,  2c,  &c. 
meet  the  arc  drk  in  the  points  k,  I,  m,  &c. ;  then,  if  connectants  be  drawn  from 
the  points  k,  I,  m,  to  the  elevation  to  meet  the  radial  lines,  we  shall  thus  obtain 
the  elevations  K,  L,  M,  of  the  corresponding  points.  Let  us  now  suppose  that  a 
sufficient  number  of  points  are.  thus  found,  and  the  curve  UK  drawn  through 
these  points;  then  UK  will  be  the  elevation  of  the  intersection  of  the  conic  and 
cylindric  surfaces  required. 

Let  us  now  construct  a  mould  for  one  of  the  joints,  suppose  for  the  second 
joint  UX,  in  the  elevation.  Draw  the  connectants  XJu,  Vv,  Ww,  Xx,  meeting 
the  line  db  prolonged  in  the  points  u,  v,  iv,  x',  and  prolong  the  connectants  Uu, 
Vv,  Wiv,  &c.  to  meet  the  plan  of  the  exterior  cylindric  surface  of  the  wall,  in 
the  points  a',  b',  c', ;  and  the  connectant  Xx  to  meet  the  plan  of  the  interme- 
diate cylindric  surface  in  the  point  d',  and  the  plan  est  of  the  inner  cylindric 
surface  on  the  point  c. 

Suppose  No.  1,  No.  2,  No.  3,  No.  4,  to  be  the  figures  of  the  moulds  of  the  first, 
second,  third,  and  fourth  joints  from  the  springing-line  ;  and  as  it  is  proposed  to 
find  the  figure  of  the  joint,  No.  2,  draw  the  straight  line  ux,  No.  2,  and  in  ux 
take  uv,  vw,  wx,  respectively  equal  to  UV,  VW,  WX,  in  the  elevation  Jig.  1. 
Draw  in  No.  2,  ua,  vb,  wc,  xe,  perpendicular  to  ux,  and  make  ua,  vb,  wc,  xd,  xe, 
respectively  equal  to  ua',  vb',  wc',  xd',  xe',  on  the  plan  Jig.  1.  Through  the 
points  a,  b,  c,  No.  2,  draw  a  portion  of  an  ellipse,  and  we  shall  have  the  edge 
of  the  joint  that  meets  the  surface  of  the  wall.  Draw  the  straight  line  cd,  No. 
2,  and  this  straight  line  will  be  the  intersection  of  the  joint  and  the  conic  sur- 
face; the  portion  de,  No.  2,  will  be  the  section  of  the  inner  cylindric  surface. 


CONSTRUCTION  OF  THE  MOULDS.  105 

The  remaining  lines  of  the  figure  of  the  mould  will  be  found  in  the  same 
manner,  and  thus  we  shall  have  the  complete  figure,  No.  2,  of  the  mould. 

Fig.  2  exhibits  the  developemcnt  of  the  soffit  of  the  horizontal  cylindritic 
surface  next  to  the  aperture,  upon  the  supposition  that  the  face  of  the  ring-stones 
are  first  wrought  in  horizontal  lines  from  the  curve  EBF,  to  meet  the  inner  hori- 
zontal cylindritic  surface,  and  afterwards  reduced  to  the  conic  form.  The 
breadth  of  the  stones  in  this  developcment  are  not  equal,  but  increase  from  each 
extreme  to  the  middle. 

The  mould  for  the  springing-stone  is  the  same  as  the  plan  of  the  jamb. 

It  will  be  necessary  to  work  the  arch-stones  into  prisms,  of  which  the  ends 
are  the  sections  of  the  stones  in  the  right  section  of  the  arch,  viz.  the  same  as 
the  compartments  adjacent  to  the  curve  in  the  elevation.  The  prisms  being 
formed,  draw  the  figure  of  the  soffit  of  the  stone  upon  the  surface  intended  for 
the  same.  Then  apply  the  joint-mould  upon  each  face  of  the  stone  intended 
for  the  joint,  and  draw  the  figure  of  the  joints;  then  reduce  the  end  of  the  stone 
which  is  to  form  a  part  of  the  face  of  the  arch  in  such  a  manner  that  when  the 
arch-stone  is  placed  in  the  position  which  it  is  to  occupy,  or  in  a  similar  situa- 
tion, a  straight  edge,  applied  in  a  horizontal  position,  may  have  all  its  points  in 
contact  with  the  surface  of  the  face  of  the  stone  now  formed.  The  face  being 
thus  formed,  the  conic  surface  must  also  be  formed  by  means  of  a  straight  edge, 
in  such  a  manner  that  all  points  of  the  straight  edge  must  coincide  with  the  sur- 
face when  the  straight  edge  is  directed  to  the  centre  of  the  cone. 


SECTION  IX. 

CONSTRUCTION  OF  THE  MOULDS  FOR  SPHERICAL  NICHES, 
BOTH  WITH  RADIATING  AND  HORIZONTAL  JOINTS,  IN 
STRAIGHT  WALLS. 

When  niches  are  small,  the  spherical  heads  are  generally  con- 
structed with  radiating  joints  meeting  in  a  straight  line,  which  pas- 
ses through  the  centre  of  the  sphere  perpendicularly  to  the  surface 
of  the  wall,  when  the  wall  is  straight  ;  but  when  it  is  erected  upon 
a  circular  plan,  the  line  of  common  intersection  of  all  the  planes  of 
the  joints  is  a  horizontal  line  tending  to  the  axis  of  the  cylindric 
wall. 

Niches  of  large  dimensions  will  be  more  conveniently  constructed 
in  horizontal  courses,  than  with  joints  which  meet  in  the  centre  of 
the  spheric  head  ;  since  in  the  latter,  the  length  and  breadth  of  the 
stones  are  always  proportional  to  the  diameter  or  radius  of  the 
sphere,  and  therefore  when  the  diameter  is  great,  the  stones  would 
be  difficult  to  procure. 

The  construction  of  niches  depend  also  upon  the  nature  and  posi- 
tion of  the  surface  from  which  they  are  recessed;  viz.  a  spherical 
niche  may  be  made  in  a  straight  wall,  either  vertical  or  inclined  ; 
or  it  may  be  constructed  in  a  circular  wall,  or  a  spherical  surface, 
such  as  a  dome. 


106 


OPERATIVE  MASONRY. 


This  subject,  therefore,  naturally  divides  itself  under  several 
heads  or  branches  ;  the  principal  are,  a  spherical  niche  in  a  straight 
wall,  with  radiating  joints  ;  a  spherical  niche  in  a  straight  wall,  in 
horizontal  courses  ;  a  spherical  niche  in  a  circular  wall,  with  radia- 
ting joints  ;  a  spherical  niche  in  a  circular  wall,  in  horizontal  cours- 
es ;  and,  a  spherical  niche  in  a  spherical  surface  or  dome. 


SECTION  X. 

EXAMPLES  OF  NICHES,  WITH  RADIATING  JOINTS,  IN 
STRAIGHT  WALLS,  AS  IN  PLATE  XIX,  Fig.  1. 

Niches  of  very  small  dimensions  will  be  easily  constructed  in 
two  equal  cubical  stones,  hollowed  out  to  the  spherical  surface,  with 
one  vertical  joint  ;  the  portion  of  the  spherical  surface,  formed  by 
both  stones,  being  one  fourth  of  the  entire  surface  of  the  sphere. 

Fig.  2  is  the  elevation,  Jig.  3  the  plan,  and  Jig.  4  the  vertical  section  perpen- 
dicular to  the  face  of  the  straight  wall  of  such  a  niche. 

The  first  operation  is  to  square  the  stone  ;  viz.  to  bring  the  head  of  each  stone 
to  a  plane  surface,  then  the  vertical  joints  and  the  upper  and  lower  beds  to 
plane  surfaces  at  right  angles  with  the  surface  which  forms  the  head. 

The  two  stones  as  hollowed  out  are  shown  at  Nos.  3  and  4.  To  show  how 
they  are  wrought,  we  will  commence  with  one  of  the  stones  after  being  brought 
to  the  cubical  form.  Let  this  stone  be  No.  3.  In  the  solid  angle  of  the  stone 
formed  by  the  head,  the  vertical  joint  and  the  lower  bed  meeting  in  the  pointy, 
apply  the  quadrantal  mould,  No.  2,  upon  each  side,  so  that  the  angular  point  of 
the  two  radiants  may  coincide  with  the  pointy,  and  one  of  the  radiants  upon 
the  arris  of  the  stone  which  joins  the  point  p ;  then  if  the  face  of  the  quadrantal 
mould  coincide  with  the  surface  of  the  stone,  the  other  radiant  line  will  also 
coincide,  because  the  angle  of  the  mould,  and  all  the  angles  of  the  faces  of  the 
stone,  are  right  angles. 

By  this  means  we  obtain  by  drawing  round  the  curved  edge  of  the  mould,  the 
three  quadrantal  arcs  abc,  agh,  and  cih.  The  superfluous  stone  being  cut  away, 
the  spherical  surface  will  be  formed  by  trial  of  the  mould,  No.  2. 

Fig.  1,  plate  20,  is  the  elevation,  and  Jig.  2,  the  plan  of  a  niche  in  a  straight 
wall. 

The  elevation,  Jig.  1,  not  only  shows  the  number  of  stones  which  must  be  odd? 
and  the  number  of  radiating  joints  which  must  in  consequence  be  one  less  than 
the  number  of  stones,  but  also  the  thickness  of  these  stones,  and  the  moulds  for 
forming  the  heads  and  opposite  sides. 

The  head  of  the  niche  being  spherical,  makes  it  a  surface  of  revolution.  It 
follows  therefore,  that  the  sections  through  the  joints  are  equal  and  similar 
figures;  hence,  if  all  the  joints  were  of  one  length,  one  mould  would  be  suffi- 
cient for  the  whole ;  but  since,  in  this  example,  they  are  of  different  lengths, 
every  two  joint  moulds  will  have  a  common  part ;  and  thus  if  the  mould  for  the 


Tl.  /  ". 


mPTCE  U  A  STIEiAI'JBIIT  ')VA  I  L,  , 


/v.  :>c. 


NICHES,  WITH  RADIATING  JOINTS 


107 


longest  joint  be  found,  each  of  the  other  moulds  will  only  bea  part  of  the  mould 
thus  found. 

In  order  to  ascertain  the  mould  for  each  joint,  the  longest  being  AD,j%".  1, 
extending  from  the  centre  to  the  extremity  of  the  stone  upon  one  side  of  the 
plan,  the  next  longest  is  AF,  extending  from  the  centre  to  the  extremity  of  the 
keystone,  and  the  shortest  AG. 

Upon  PQ,,fig.  1,  make  AF  equal  to  AF",  and  AG  equal  to  AG'.  Perpendicu- 
lar to  PQ,  drawn  Dd,  Ffi,  Gg,  meeting  the  front  line  RSof  the  plan,  fig.  2,  in  the 
points  d,f,  g,  intersecting  the  back  line  of  the  stone  in  the  points  m,  n,  o  :  then 
will  No.  1,  kikedm  be  the  mould  for  the  first  stone  raised  upon  the  plan,  hikefn 
the  mould  for  the  joint  on  each  side  of  the  keystone,  hikego  the  mould  for  the 
first  stone  above  the  springing  line.  These  moulds  are  shown  separately  at 
I,  II,  III,  and  identified  by  similar  letters. 

Nos.  1,  2,  3,  exhibit  the  first,  second,  and  third  stones  of  the  niche  as  if  wrought 
to  the  form  of  the  spherical  surface ;  No.  3  being  the  keystone  ;  therefore  the 
two  remaining  stones  are  wrought  in  a  reverse  order  to  the  stones  exhibited  at 
No.  1  and  No.  II. 

The  first  part  of  the  operation  is  to  work  the  stones  into  a  wedge-like  form,  so 
that  the  right  section  of  these  stones  may  correspond  to  the  figures  formed  by 
the  radiations  of  the  joints  to  the  centre  A,  fig.  1,  and  by  the  horizontal  and  ver- 
tical joints  of  the  stones  adjacent  to  those  which  form  the  niche  ;  for  this  pur- 
pose, two  moulds  for  each  head  will  be  necessary,  viz.  one  whole  mould  must  be 
made  for  each  stone,  and  one  mould  for  the  part  within  the  circle,  which  will 
apply  to  every  stone,  in  order  to  form  the  extent  of  the  part  within  the  recess  : 
thus  a  mould  formed  to  the  sectoral  frustrum  EE'K'K  in  the  elevation,  fig.  1, 
will  apply  alike  to  all  stones,  as  will  be  shown  presently. 

The  next  thing  is  to  form  the  moulds  K'KDSG',  K'K'G'TF"  and  K"K"F"F" 
of  the  heads  ;  the  application  of  these  moulds  is  as  follows  : — 

Having  wrought  the  under  bed,  the  head  and  back  of  each  stone,  and  having 
formed  a  draught  next  to  the  edge  of  the  bed,  upon  the  side  which  is  to  lie  upon 
the  cylindric  part  in  the  centre,  at  a  right  angle  with  the  head,  apply  the  mould 
K'KDSG',  fig.  1,  upon  the  head  of  the  stone,  No.  1,  so  that  the  straight  edge 
KD  may  be  close  upon  the  bed  of  the  stone,  and  draw  by  the  other  edges  of  the 
mould  ;  thus  applied  the  figure  r'rdsg ;  and,  in  the  same  line  rd,  close  to  the  bed, 
apply  the  mould  K'KEE',  fig.  1,  and  by  the  other  edges  of  this  mould  draw  the 
figure  r'ree'.  Apply  the  mould  K'KDSG',  to  the  opposite  or  parallel  side  of  the 
stone,  close  to  the  bed,  and  draw  a  similar  and  equal  figure  ns  was  done  by  the 
same  mould  when  it  was  applied  to  the  head  ;  this  done,  work  the  upper  bed  of 
the  stone. 

Proceed  in  like  manner  with  the  stones  exhibited  at  No.  2  and  No.  3,  and  sim- 
ilarly with  the  stones  on  the  left-hand  side  of  the  arch  ;  the  stones  No.  1  and 
No.  2  answering  to  those  on  the  right  hand  of  the  keystone. 

In  order  to  show  the  application  of  the  moulds  marked  I.  II.  III.  at  the  bot- 
tom of  the  plate,  taken  from  the  plan,  fig.  2 ;  the  mould  I.  applies  to  the  under 
bed  of  the  stone,  No.  I ;  the  next  mould  II.  applies  upon  the  upper  bed  of  No.  1, 
and  upon  the  under  bed  of  No.  2;  and  the  mould  III.  applies  upon  the  upper 
bed  of  No.  2,  and  upon  each  side  of  the  keystone,  No.  3. 


108 


OPERATIVE  MASONRY. 


As  every  arch  has  both  a  right  and  left  hand  side,  and  as  every  joint  is  formed 
by  the  surfaces  of  two  stones,  every  mould  has  four  applications,  one  on  each  of 
the  four  stones. 

In  order  to  render  these  applications  of  the  moulds  I.  II.  III.  as  clear  as  pos- 
sible, the  corresponding  situations  of  the  points  marked  upon  each  stone  by  each 
respective  mould,  are  marked  by  similar  letters  to  those  on  the  moulds  I.  II.  III. 
or  their  correspondents  on  the  plan,  fig.  2,  viz.  on  the  under  bed  of  the  stone, 
No.  1,  will  be  found  the  letters  h,  i,  k,  e,  d,  to,  as  in  the  mould  I. ;  upon  the  under 
bed  of  No.  2,  will  be  found  h',  i',  k',  e\g',  o  ;  as  also  upon  the  upper  bed,  of  No. 
I,  i\  k',e',  g',  and  upon  the  right  hand  side  of  the  keystone,  No.  3,  will  be  found 
the  letters  h",  k",  t",f",  n',  as  also  similar  letters  upon  the  upper  bed,  No.  2, 
to  those  of  the  mould  III. 

ARCH,  WITH  SPLAYED  JAMBS. 

To  find  the  angles  of  the  joints  formed  by  the  front  and  intrados 
of  an  elliptical  arch,  erected  on  splayed  jambs. 

No.  1,  on  fig.  3,  is  the  place  of  the  impost ;  No.  2,  the  elevation. 

The  impost  A'B'C'D  E  is  the  first  bed  ;  f  g  hik,  the  second  ;  I  to  n  o  p,  the 
third  ;  q  r  st  u,  the  fourth  ;  v  w  x  y  z,  the  fifth.  The  other  beds  are  the  same  in 
reverse  order.  The  breadth  of  all  these  beds  is  the  same  as  that  of  the  arch 
itself.  The  lengths  kK,  ?iP,  s\J,  xZ,  of  the  front  lines  of  the  moulds  of  the  beds 
are  respectively  equal  to  the  lines  HF,  NL,  SQ,  X  V,  on  the  face  of  the  arch. 
And  also,  hg,  nm,  sr,  xw,  on  the  parts  of  the  moulds  equal  to  the  corresponding 
distances  HC,  NM,  SK,  XW,  on  the  face  of  the  arch.  The  distances  kf,  pi,  ug, 
rvf  are  equal  to  the  perpendicular  part  AE  of  the  impost. 


SECTION  XI. 

EXAMPLES  OF  NICHES  IN  STRAIGHT  WALLS  WITH  HORIZON- 
TAL COURSES,  AS  IN  PLATE  XXI,  Fig.  1. 

Let  Jig.  2  represent  a  niche  with  horizontal  courses,  No.  1  being  the  elevation, 
exhibiting  three  arch-stones  on  each  side  of  the  keystone,  and  No.  2  the  plan, 
consisting  of  two  stones,  making  together  a  semicircle,  each  being  one  quadrant. 

The  heads  of  the  stones  in  the  wall,  on  the  right-hand  side  of  the  arch,  which 
also  form  a  portion  of  the  concave  surface,  are  ABCDE,  FDCGHM,  MGKLM, 
and  the  key-stone  LKKL.  Round  each  of  these  figures  circumscribe  a  rect- 
angle, so  that  two  sides  may  be  parallel  and  two  perpendicular  to  the  horizon  .* 
thus  round  the  head  of  the  stone  ABCDE  circumscribe  the  rectangle  ANOE' 
round  the  figure  FDCGMI,  the  head  of  the  second  stone,  circumscribe  the  rect- 
angle PQRI,  &c. 

Draw  the  straight  lines  am,  and  ai,  Jig.  3,  No.  1,  forming  a  right  angle  with 
each  other ;  from  the  point  a  as  a  centre,  with  the  radius  d  b  c  describe 
the  arc  cc',  meeting  the  lines  am  and  ai  in  the  points  c,c'. 


NICHES  IN  STRAIGHT  WALLS. 


109 


Let  the  quadrangular  figure  hgfie,  No.  1,  be  considered  as  the  upper  bed  of  a 
stone,  which,  as  well  as  the  lower  bed,  is  wrought  smooth,  these  two  surfaces 
being  parallel  planes  at  a  distance  from  each  other  equal  to  the  line  AE  or  CD, 
Jig.  2.  Moreover,  let  mcc'bb,  dd  be  considered  as  a  mould  made  to  the  figure  before 
described  and  laid  flat  on  the  upper  bed  of  the  stone  in  its  true  position,  the 
points  c,c'  of  the  mould  being  brought  as  near  to  the  side  he  as  will  just  leave  a 
sufficient  quantity  of  stone,  in  order  to  work  it  complete.  By  the  edges  of  the 
mould  thus  placed  draw  the  curve  cc',  the  straight  lines  c??iand  c'i,  and  the  rough 
edges  ik  and  ml. 

Perpendicular  to  the  upper  bed,  and  along  the  arc  cc',  cut  the  stone  so  as  to 
form  a  surface  perpendicular  to  the  upper  bed,  and  the  surface  thus  formed  will 
necessarily  be  cylindric ;  through  each  of  the  straight  lines  cm  and  c'i  cut  a 
surface  perpendicular  to  the  said  upper  bed,  and  these  surfaces  will  be  the  planes 
of  the  vertical  joints,  and  will  be  at  a  right  angle  with  each  other ;  then  with  a 
guage,  of  which  the  head  is  made  to  the  cylindric  surface,  and  which  is  set  to 
the  distance  OD,  fig,  2,  No.  1,  draw  the  curve  line  dd  on  the  upper  bed  of  the 
stone.  Upon  the  lower  bed  of  the  stone,  with  the  guage  set  to  the  distance  NB, 
draw  the  arc  bb'. 

The  thickness  of  the  stone  is  exhibited  at  No.  2,  fig.  3,  the  upper  bed  being- 
represented  by  the  line  fir,  and  the  lower  bed  by  the  line  qu,  so  that  nr  and  qu 
are  parallel  lines,  the  distance  between  them  being  equal  to  the  thickness  of  the 
stone,  viz.  equal  to  AE,  fig.  2,  No.  1.  Lastly,  with  a  plane  or  common  guage 
set  to  the  distance  NC,  fig.  2,  No.  1,  draw  the  line  cc  on  the  cylindric  surface, 
fig.  3,  No.  1. 

Now,  in  fig.  3,  the  line  dd',  No.  2,  represents  the  arc  dd',  No.  1 ;  cc',  No.  2,  rep- 
resents the  arc  cc',  No.  1 ;  and  W,  No.  2,  represents  the  arc  bb,  No.  1 :  so  that 
the  stone  must  be  cut  away  between  the  line  dd'  on  the  upper  bed,  and  cc'  on  the 
cylindric  surface,  by  means  of  a  straight  edge,  so  as  to  form  a  conic  surface  ; 
this  may  be  done  by  setting  a  bevel  to  the  angle  EDC,  fig.  2,  No.  1.  The  conic 
surface  thus  formed  will  be  one  side  of  the  joint  within  the  spheric  surface. 

Again,  cut  away  the  stone  between  the  line  cc'  on  the  cylindric  surface,  and 
the  arc  bb'  before  drawn  on  the  lower  bed  by  means  of  the  curved  bevel  shown 
at  A,  fig.  2,  No.  2,  so  as  to  form  a  spherical  surface.  This  may  be  done  in  the 
most  complete  manner,  by  applying  the  straight  side  of  the  curved  bevel  B,fig. 
2,  No.  2,  to  the  under  bed  of  the  stone,  so  as  to  be  perpendicular  to  the  curve  ; 
then,  if  the  curved  edge  coincide  at  all  points,  the  surface  between  these  lines 
will  be  spherical,  and  will  form  that  portion  of  the  head  of  the  niche  which  is 
contained  on  the  stone. 

In  the  same  manner  all  the  other  stones  may  be  cut  to  the  form  required. 

Fig.  4  exhibits  the  stone  in  the  middle  of  the  second  course,  and  fig.  5  the 
stone  on  the  left  of  the  same  course  in  the  angle,  which  last  stone  is  one  half  of 
the  stone  represented  by  fig.  4.  • 

Fig.  6  exhibits  the  left-hand  stone  of  the  third  course,  and  fig.  7  the  keystone, 
which  is  wrought  into  the  frustrum  of  a  cone  to  a  given  heighten  order  to  agree 
with  the  circular  courses ;  and  to  prevent  any  tendency  of  the  keystone  from 
coming  out  of  its  place,  the  upper  part  is  cut  into  the  frustrum  of  a  pyramid. 


no 


OPERATIVE  MASONRY. 


Plate  XXII,  jig.  1,  represents  a  spheric  headed  niche  in  a  straight  wall  with 
four  arch-stones  on  each  side  of  the  keystone,  and  therefore,  also,  with  four 
horizontal  courses;  and  as  the  joints  are  broken,  if  we  begin  the  first  course 
with  four  whole  stones,  as  exhibited  on  the  plan,  No.  2,  the  next  course  will 
consist  of  three  whole  stones  and  two  half  stones  in  one  in  each  angle.  As  the 
stones  are  here  in  this  example  projected  on  the  plan  as  well  as  on  the  elevation, 
the  elevation,  No.  1,  not  only  exhibits  the  number  of  courses,  but  the  number  of 
stones  also  in  each  course. 

Fig.%  represents  a  spheric  headed  niche  in  four  courses  besides  the  keystone. 
No.  2,  the  ground  plan  of  No.  1. 

Jt  may  be  observed  once  for  all,  that  the  greater  the  dimensions  of  a  niche, 
the  greater  must  also  be  the  number  of  courses  in  the  height. 

The  principles  for  cutting  the  stones  of  these  niches,  is  the  same  as  has  already 
been  explained  for  Plate  XXI. 


SECTION  XII. 

CONSTRUCTION  OF  THE  MOULDS,  AND  FORMATION  OF  THE 
STONES,  FOR  DOMES  UPON  CIRCULAR  PLANES,  AS  IN  PLATE 
XXIII,  Fig.  1^2. 

ON  THE  CONSTRUCTION  OF  SPHERICAL  DOMES. 

Since  walls  and  vaults  are  generally  built  in  horizontal  courses, 
the  sides  of  the  coursing  joints  in  spherical  domes  are  the  surfaces 
of  right  cones,  having  one  common  vortex  in  the  centre  of  the 
spheric  surface,  and  one  common  axis  ;  hence  the  conic  surfaces  will 
terminate  upon  the  spheric  surface  in  horizontal  circles  :  again,  be- 
cause the  joints  between  any  two  stones  of  any  course  are  in  vertical 
planes  passing  through  the  centre  of  the  spheric  surface,  the  planes 
passing  through  all  the  joints  between  every  two  stones  of  every 
course  will  intersect  each  other  in  one  common  vertical  straight 
line  passing  through  the  centre  of  the  spheric  surface. 

The  line  in  which  all  the  planes  which  pass  through  the  vertical 
joints  intersect,  is  called  the  axis  of  the  dome. 

Because  a  straight  line  drawn  through  the  centre  of  a  spheric  sur- 
face, perpendicular  to  any  plane  cutting  the  spheric  surface,  will  in- 
tersect the  cutting  plane  in  the  centre  of  the  circle  of  which  the  cir- 
cumference is  the  common  section  of  the  plane  and  spheric  surface, 
the  axis  of  the  dome  will  intersect  all  the  circles  parallel  to  the 
horizon  in  their  centre. 

The  circumference  of  the  horizontal  circle,  which  passes  through 
the  centre  of  the  spheric  surface,  is  called  the  equatorial  circumference, 
and  any  portion  of  this  circumference  is  called  an  equatorial  arc. 

The  circumferences  of  circles,  which  are  parallel  to  the  equatorial 
circle,  are  called  parallels  of  altitude,  and  any  portions  of  these  cir- 
cumferences are  called  arcs  of  the  ]oarallels  of  altitude. 


CONSTRUCTION  OF  THE  MOULDS. 


Ill 


The  intersection  of  the  axis,  and  the  spheric  surface,  is  called  the 
pole  of  the  dome. 

The  arcs  between  the  pole  and  the  base  of  the  dome,  of  the  circles 
formed  on  the  spheric  surface  by  the  planes  which  pass  along  the 
axis,  are  called  meridians,  and  any  portions  of  these  meridians  arc 
called  meridional  arcs. 

The  conical  surfaces  of  the  coursing-joints  terminate  upon  the 
spheric  surface  of  the  dome  in  the  parallels  of  altitude,  and  the  sur- 
faces of  the  vertical  joints  terminate  in  the  meridional  arcs. 

Hence  in  domes,  where  the  extrados  and  intTados  are  concentric 
spheric  surfaces,  to  apparent  sides  of  each  stone  contained  by  two  me- 
ridional arcs,  and  the  arcs  of  two  parallel  circles  are  spheric  rectan- 
gles, the  two  sides  which  form  the  vertical  joints  are  equal  and  simi- 
lar frustruins  of  circular  sectors,  and  the  other  two  sides  forming 
the  beds  are  frustrums  of  sectors  of  conic  surfaces. 

In  the  execution  of  domes,  since  the  courses  are  placed  upon  coni- 
cal beds  which  terminate  upon  the  curved  surfaces  in  the  circumfer- 
ences of  horizontal  circles,  they  are  comprised  between  horizontal 
planes,  and  therefore  may  be  said  to  be  horizontal.  Hence  the 
general  principle  of  forming  the  stones  of  a  niche  constructed  in 
horizontal  courses  may  likewise  be  applied  in  the  construction  of 
domes. 

Each  of  the  stones  of  a  course  is  first  formed  into  six  such  faces 
as  will  be  most  convenient  for  drawing  the  lines,  which  form  the 
arrises  between  the  real  faces.  Two  of  these  preparatory  faces  are 
formed  into  uniform  concentric  cylindric  surfaces,  passing  through 
the  most  extreme  points  of  the  axal  section  of  the  course  in  which 
the  stone  is  intended  to  be  placed,  the  axis  of  the  dome  being  the 
common  axis  of  the  two  cylindric  surfaces  of  every  course. 

Two  of  the  other  surfaces  are  so  formed  as  to  be  in  planes  perpen- 
dicular to  the  axis  of  the  dome,  and  to  pass  through  the  most  extreme 
points  of  the  axal  or  right  sections  of  the  course,  as  was  the  case  with 
the  two  cylindric  surfaces. 

The  extreme  distance  of  the  two  remaining  surfaces  depends  upon 
the  number  of  stones  in  the  course.  These  surfaces  are  in  planes 
passing  through  the  axis,  and  are  therefore  perpendicular  to  the 
other  two  planes.  As  these  plan.es,  which  pass  through  the  axis, 
from  the  vertical  joints,  they  remain  permanent,  and  undergo  no 
alteration  except  in  the  boundary,  which  is  reduced  to  the  figure  of 
the  axal  section  of  the  course. 

In  order  to  find  the  terminating  lines  of  the  last  and  permanent 
faces,  draw  the  figure  of  the  section  of  the  course  upon  one  of  the 
two  vertical  joints  in  its  proper  position,  then  two  of  the  corners  of 
the  mould  will  be  in  the  two  cylindric  surfaces,  one  point  in  the 
one,  and  the  other  in  the  other,  and  the  two  remaining  corners  of 
the  mould  will  be  in  the  two  surfaces  which  are  perpendicular  to 
the  axis,  one  point  of  the  mould  being  in  the  one  plane  surface,  and 
the  other  point  in  the  other  plane  surface. 
15 


112  OPERATIVE  MASONRY. 

Draw  a  line  on  each  of  the  cylindric  surfaces  through  the  point 
where  the  axal  section  meets  the  surface  parallel  to  one  of  the  circu- 
lar edges,  and  the  line  thus  drawn  on  each  of  the  cylindric  surfaces 
will  be  the  arc  of  a  circle  in  a  plane  perpendicular  to  the  axis  of  the 
two  cylindric  surfaces,  and  will  be  equal  and  similar  to  each  of  the 
edges  of  the  cylindric  surface  to  which  it  is  parallel  ;  but  in  the 
first  course  of  a  hemispheric  dome,  there  will  be  no  intermediate 
line  on  the  convex  side,  since  the  circular  arc  terminating  the  lower 
edge,  will  also  be  the  arris  line  of  the  convex  spheric  surface  and  the 
lower  bed  of  the  stone,  which,  in  this  course,  is  a  plane  surface. 

In  all  the  intermediate  courses  of  the  dome  between  the  summit 
and  the  first  coarse,  the  line  drawn  on  the  convex  cylindric  surface 
will  be  the  arris  line  between  the  convex  spheric  surface,  and  the 
convex  conic  surface  which  forms  the  lower  bed  of  the  stone  ;  and 
in  all  the  courses  from  the  base  to  the  summit,  the  line  drawn  on  the 
concave  cylindric  surface  will  be  the  arris  line  between  the  concave 
conic  surface  forming  the  upper  bed,  and  the  concave  spheric  surface 
of  the  stone,  which  concave  surface  will  form  a  portion  of  the  inte- 
rior surface  of  the  dome. 

On  the  upper  plane  surface  of  each  stone  to  be  wrought  for  the 
first  course,  draw  a  line  parallel  to  one  of  the  circular  edges  ;  but  in 
each  of  the  stones  for  the  intermediate  courses  between  the  first 
course  and  the  key-stone  at  the  summit,  draw  a  line  on  each  of  the 
planes  which  are  perpendicular  to  the  axis  parallel  to  either  of  the 
edges  of  the  face  upon  which  the  line  is  made  through  the  common 
point  in  the  vertical  plane  of  the  joint  and  the  horizontal  plane,  then 
the  line  drawn  on  the  top  of  every  stone  will  be  the  arris  line  between 
the  convex  spheric,  and  the  concave  conic  surfaces  to  be  formed, 
and  the  line  drawn  on  the  under  side  of  any  stone  in  each  of  the 
intermediate  courses  will  be  the  arris  between  the  convex  conic  and 
the  concave  spheric  surfaces  to  be  formed  ;  that  is,  between  the  sur- 
faces which  will  form  the  lower  bed  and  a  portion  of  the  interior 
surface  of  the  dome. 

Draw  the  form  of  the  section  of  the  course  upon  the  plane  of  the 
other  joint,  so  that  the  corners  of  the  quadrilateral  figure  thus  drawn 
may  agree  with  the  four  lines  drawn  on  the  two  cylindric,  and  on 
the  two  parallel  plane  surfaces. 

Lastly,  reduce  the  stone  to  its  ultimate  figure  by  cutting  away 
the  parts  between  every  two  adjacent  lines  which  are  to  form  the 
arrises  between  every  two  adjacent  surfaces,  until  each  surface  ac- 
quire its  desired  form. 

Each  of  the  spherical  surfaces  must  be  tried  with  a  circular  edged 
rule,  in  such  a"  manner  that  the  plane  of  curve  must  in  every  appli- 
cation be  perpendicular  to  each  of  the  arris  lines,  the  mould  for  the 
convex  spheric  surface  being  concave  on  the  trying  edge  which  must 
be  a  portion  of  the  convex  side  of  the  section,  1,  and  the  mould 
for  the  concave  side  convex  on  the  trying  edge,  and  a  portion  of  the 
concave  arc  forming  the  inside  of  the  section. 

The  two  conical  surfaces  of  the  beds,  and  the  two  plane  surfaces 
of  the  vertical  joints,  must  be  each  tried  with  a  straight  edge,  in 


CONSTRUCTION  OF  THE  MOULDS. 


113 


such  a  manner  that  the  trying  edge  must  always  be  so  placed  as  to 
be  in  a  plane  perpendicular  to  each  of  the  circular  terminating  arcs  ; 
so  that  the  surfaces  between  these  arcs  must  always  be  prominent 
until  the  trying  edge  coincide  with  the  two  circular  edges,  and  every 
intermediate  point  of  the  trying  edge  with  the  surface. 

Fig.  3,  Let  Abcdef .  .  .  .  Y,  be  the  exterior  curve  of  the  section  divided  into 
the  equal  parts  Ab,  be,  cd,  &c.  at  the  points  b,  c,  &c.  so  that  each  of  the  chords 
Ab,  be,  cd,  &c.  may  be  equal  to  the  breadth  of  the  stones  in  each  of  the  circular 
courses  ;  also  let  ghijkl  ....  X,  be  the  inner  curve  of  the  section,  divided  like- 
wise into  the  equal  arcs  gh,  hi,  ij,  &c,  by  the  radiating  lines  bh,  ci,  &c. ;  hence 
Abhg  is  a  right  section  of  the  first  course;  and,  therefore,  the  figure  of  the  joint 
at  each  end  of  every  stone  in  the  first  course  ;  likewise  bcih  is  the  right  section 
of  the  second  course  ;  and,  therefore,  the  figure  of  the  joint  at  each  end  of  every 
stone  in  the  second  course. 

Since  the  entire  exterior  curve  of  the  axal  section  of  the  dome  is  divided  into 
equal  parts  alike  from  the  basis  on  each  side  of  the  section  ;  and  since  the  exte- 
rior and  interior  sides  of  the  section  are  each  a  semicircular  arc,  and  described 
from  the  same  centre  ;  and  since  the  dividing  lines  bh,  ci,  &c.  radiate  to  this 
centre,  all  the  sections  of  the  courses,  and  the  boundaries  of  the  vertical  joints 
will  be  equal  and  similar  figures;  and,  therefore,  a  mould  made  to  the  figure  of 
the  section  of  any  course  will  serve  for  the  vertical  joints  of  all  the  stones. 

Fig.  4  exhibits  one  fourth  part  of  the  plan  of  the  convex  side  of  the  dome 
showing  the  number  of  courses,  and  the  number  of  stones  in  each  quarter-course, 
there  being  three  stones  of  equal  length  in  each  quarter-course. 

In  the  first  or  bottom  course,  mnop  is  the  plan  of  the  convex  side  of  one  of 
the  stones,  and  m'n'o'p'  the  plan  of  the  concave  side  of  the  same  stone ;  and,  in 
the  second  course,  qrst  is  the  plan  of  the  convex  side  of  one  of  the  stones,  and 
q'r's't'  is  the  plan  of  the  concave  side  of  the  same  stone;  so  that  in  the  first  course 
mno'p'  is  the  figure  of  the  top  and  bottom  of  one  of  the  ring-stones,  po  is  the 
intermediate  line  on  the  top,  and  m'n'  that  on  the  bottom,  and  so  on  for  the  re- 
maining stones. 

All  the  stones  of  any  course  being  equal  and  similar  solids,  and  alike  situated, 
the  same  mould  which  serves  to  execute  any  stone  of  any  one  course  will  serve 
to  execute  every  stone  of  that  course ;  but  every  course  must  have  a  different 
set  of  moulds  from  those  of  another,  except  the  figures  of  the  vertical  joints, 
which  will  be  all  found  by  one  mould,  as  has  been  already  observed. 

The  reader,  who  has  a  competent  knowledge  of  the  construction  of  niches  in 
horizontal  courses,  will  not  be  at  any  great  loss  to  understand  the  construction  of 
domes  ;  or  if  the  construction  of  domes  is  well  understood,  he  cannot  be  at  any 
loss  to  comprehend  the  construction  of  niches ;  however,  as  there  are  many  ob- 
servations respecting  the  construction  of  domes  that  do  not  apply  to  niches, 
particularly  as  the  dome  in  the  present  article  has  two  apparent  sides,  in  order  to 
prevent  the  reader  from  wasting  his  time  in  referring  to  both  articles,  we  shall 
here  conduct  him  through  the  formation  of  one  of  the  stones  in  the  first  two 
courses,  the  figure  of  the  stones  in  the  remaining  courses  being  found  in  a  similar 
manner. 


• 


114 


OPERATIVE  MASONRY. 


In  fig.  3,  draw  AD  perpendicular  to  the  ground-line  AY,  and  through  h  draw 
BC  also  perpendicular  to  the  ground-line  AY.  Now  AB  as  well  as  Ag  being 
upon  the  ground-line,  therefore  to  complete  the  rectangle  ABCD,  so  as  to  cir- 
cumscribe the  section  Abhg,  and  to  have  two  vertical  and  two  horizontal  sides, 
draw  through  the  point  b  the  remaining  side  DC  parallel  to  AY. 

The  rectangle  ABCD  is  the  section  of  a  circular  course  of  stone,  or  that  of  a 
ring  contained  by  two  vertical  concentric  uniform  cylindric  surfaces  and  by  two 
horizontal  plane  rings,  the  radius  of  the  concave  cylindric  surface  being  aB,  and 
the  radius  of  the  convex  cylindric  surface  being  aA,  and  the  height  of  the  ring 
being  AD  or  BC. 

Make  a  mould  to  the  plan  of  one  of  the  stones  in  the  first  course,  that  is,  to 
mnop,  Jig.  4. 

From  any  point  y,  fig.  5,  with  a  radius  zm,  Jig.  4,  or  the  radius  aA,  fig.  3,  de- 
scribe the  arc  mn.  Make  the  arc  mn,  Jig.  5,  equal  to  the  arc  mn,  fig.  4,  and  draw 
the  lines  mu  and  nv  radiating  to  the  point  y.  Again,  from  the  centre  y,  and  with 
the  radius  aB,fg.  3,  describe  the  arc  vu. 

Make  a  face-mould  to  mnvu,  and  this  mould  will  serve  for  drawing  the  figure 
of  the  two  horizontal  surfaces  of  each  stone  in  the  first  or  bottom. 

To  cut  one  of  the  stones  in  the  first  course  to  the  required  form : — Reduce  the 
stone  from  one  of  the  sides  till  the  surface  becomes  a  plane.  Apply  the  mould 
made  to  the  figure  mnvu  on  this  surface,  which  is  one  of  the  two  horizontal 
faces,  and  having  drawn  the  figure  of  the  mould,  reduce  the  stone  so  as  to  form 
three  of  the  arris  lines  of  the  faces,  which  are  to  be  vertical,  and  these  arrises 
•will  be  square  to  the  face  already  wrought.  On  each  of  the  three  arrises  thus 
formed,  set  the  height  of  the  stone  from  the  plane  surface  already  made  ;  reduce 
the  substance  till  the  surface  becomes  a  plane  parallel  to  that  first  formed. 

Apply  then  the  face  mould  mnvu,  upon  the  plane  surface  last  wrought,  so  that 
three  points  of  the  mould  may  join  the  corresponding  points  in  the  meeting  of 
the  three  arrises,  and  having  drawn  the  figure  of  the  mould  upon  the  second 
formed  face,  run  a  draught  on  the  outside  of  each  line  upon  each  of  the  inter- 
mediate surfaces  from  each  of  the  parallel  faces.  So  that  there  will  be  four 
draughts  receding  from  the  face  first  formed,  and  four  receding  from  the  face 
last  formed,  and  that  upon  the  whole,  including  the  two  draughts  upon  each 
side  of  each  of  the  four  perpendicular  arrises,  there  will  be  sixteen  in  all. 

The  two  draughts  along  the  edges  of  the  convex  cylindric  surface  to  be  formed, 
must  be  tried  with  a  concave  circular  rule,  made  to  the  form  of  the  arc  mn,  fig. 
4,  and  the  two  draughts  along  the  edges  of  the  concave  cylindric  surface,  must 

be  tried  with  a  convex  circular  rule  made  to  the  form  of  the  arc  po,  Jig.  4. 

Moreover,  the  two  draughts  which  are  made  along  each  of  the  edges  of  each 
opposite  intermediate  plane  surface,  must  be  tried  with  a  straight  edge. 

Having  regularly  formed  the  draughts,  so  that  the  circular  and  straight  edges 
of  each  of  the  three  rules  may  coincide  in  all  points  with  the  bottom  surface  of 
each  respective  draught,  and  with  the  arris  line  at  each  extremity,  the  workman 

may  then  cut  away  the  superfluous  parts  of  the  stone,  as  far  as  he  can  discern 

to  be  just  prominent,  or  something  raised  above  the  four  draughts,  bordering 

the  four  edges  of  each  of  these  surfaces. 


CONSTRUCTION  OF  THE  MOULDS. 


115 


The  rough  part  of  the  operation  being  done,  each  of  the  four  intermediate 
faces  may  be  brought  to  a  smooth  surface  and  to  the  required  form,  by  means  of 
a  common  square ;  the  face  of  coincidence  of  the  stock,  or  thick  leg,  being  ap- 
plied upon  one  of  the  two  parallel  faces,  and  the  thin  leg,  called  the  blade,  to  the 
surface  of  the  stone,  in  the  act  of  reducing,  until  it  has  acquired  the  figure  de- 
sired, or  the  two  cylindric  surfaces  may  also  be  tried  by  means  of  circular  edged 
rules,  the  edge  of  each  rule  being  placed  so  as  to  be  parallel  to  one  of  the  parallel 
faces  ;  a  concave  circular  edge  being  applied  upon  the  convex  side,  and  a  convex 
circular  edge  upon  the  concave  side. 

The  six  faces  which  contain  the  solid  being  thus  formed,  we  shall  now  pro- 
ceed to  find  the  upper  arris  : — for  this  purpose  apply  the  mould  made  to  the  form 
mnop,  fig.  4,  upon  the  top  of  the  stone  drawn  by  the  means  of  the  mould  mnvu, 
fig-  5. 

Suppose  mnvu,  fig.  5,  to  be  the  figure  drawn  on  the  top  of  the  stone  itself,  by 
means  of  the  mould  made  to  mnvu ;  and  mnop,  fig.  5,  to  be  the  mould  made 
from  mnop,  fig.  4.  Lay  the  edge  mn,  fig.  4,  upon  the  edge  m?i,  fig.  5,  on  the  top 
of  the  stone,  so  that  the  equal  circular  arcs  may  coincide  in  all  their  points ;  and 
draw  the  line  op  along  the  concave  edge  of  the  mould,  and  op  will  be  the  arris 
line  of  the  spherical  and  conical  surfaces  which  are  yet  to  be  formed. 

Let  the  rectangle  mnn'm',  fig.  6,  be  the  elevation  of  the  convex  cylindric  sur- 
face of  the  same  stone,  projected  on  a  plane  parallel  to  each  of  the  chords  of 
the  circular  arcs,  and  to  one  of  the  straight  arrises  of  this  surface;  the  straight 
line  mn  representing  the  upper  circular  edge,  mm,  nn'  the  two  vertical  arrises  ; 
so  that  the  convex  spherical  surface  is  terminated  at  the  top  by  the  arc  op  and  at 
the  bottom  by  the  arc  n'm'. 

Let  the  rectangle  nmm'n',  fig.  7,  be  the  elevation  of  the  concave  cylindric  face 
projected  on  a  plane,  parallel  to  one  of  the  chords  of  one  of  the  circular  bounda- 
ries, and  to  one  of  the  straight-lined  boundaries  of  this  face ;  then  the  upper 
and  lower  planes  will  be  projected  into  the  parallel  lines  nm,  n'm'.  Therefore 
all  the  lines  of  each  of  these  three  planes  will  be  projected  upon  the  lines  nm, 
n'm',  and  as  the  rectilineal  figure  formed  by  the  two  chords  and  the  two  straight 
lines  is  parallel  to  the  plane  of  projection,  it  will  be  projected  into  an  equal  and 
similar  figure ;  therefore  the  projected  figure  is  a  rectangle,  and  the  sides  nm 
n'm  are  equal  to  each  other,  and  to  the  chords  of  the  two  circular  arcs  ;  and  the 
lines  m'm,  nn'  are  each  equal  to  the  height  of  the  hollow  cylinder,  or  equal  to  the 
distance  between  the  parallel  planes. 

Hence  the  concave  surface  will  be  projected  also  into  a  rectangle,  and  the 
middle  of  the  chords  of  the  arcs  terminating  the  parallel  edges  of  the  concave 
surface  upon  the  middle  of  the  chords  of  the  arcs,  terminating  two  of  the  op- 
posite edges  of  the  convex  surface,  as  also  the  two  opposite  parallel  straight- 
lined  sides  in  the  height  of  the  solid,  will  be  projected  into  straight  lines  equi- 
distant from  the  projections  of  the  corresponding  lines  in  the  height  of  the  solid 
on  the  convex  side. 

Therefore,  the  stmight  lines  nn',mm',  vv',  uu',  are  all  equal  to  the  height  of  the 
hollow  cylindric  solid,  or  equal  to  the  distance  between  the  parallel  planes  and 
the  distance  between  the  lines  nn',  vv',  equal  to  the  distance  between  the  lines 
mm',  uu'. 


( 

116  OPERATIVE  MASONRY. 

To  form  the  common  termination  between  the  upper  conical  and  the  lower 
spherical  surfaces,  let  vv\  u'u,  represent  the  concave  cylindric  surface;  and, 
therefore  vv',uu',  will  represent  the  opposite  circular  arcs,  which  terminate  two 
of  the  sides  of  this  concavity.  Upon  this  surface  draw  the  lines  v"  u",  parallel 
to  the  circular  edge  vu,  on  the  top  at  the  distance  hC,fig.  3,  and  the  line  v",  u" 
will  be  the  arris  now  required  between  the  concave  conic  surface  at  the  top,  and 
the  concave  spheric  surface.    These  two  surfaces  being  as  yet  to  be  formed. 

To  form  the  remaining  and  common  termination  of  the  concave  spherical 
surface,  and  the  lower  or  level  bed  of  the  stone : — Draw  a  circular  arc  on  the 
level  surface,  underneath  parallel  to  the  circular,  to  the  circular  edge  on  the 
lower  edge  of  the  concave  cylindric  surface,  and  this  line  will  be  the  remaining 
arris  required. 

The  two  cylindric  surfaces,  and  the  upper  plane  surface,  are  entirely  cut  away ; 
but  the  intermediate  line  drawn  on  the  top,  and  that  drawn  on  each  cylindric 
surface,  remain,  as  well  as  the  outer  edge  of  the  lower  bed. 

To  form  the  intermediate  faces  of  the  stone,  into  the  two  upper  and  lower 
conical  beds,  and  into  the  two  apparent  concave  and  convex  spherical  surfaces: 
Reduce  each  side  of  the  solid  as  near  to  the  required  surface  as  possible,  so  that 
all  the  intermediate  parts  between  the  arrises  or  lines  drawn  on  the  former  faces, 
may  be  prominent. 

Suppose  then,  that  we  proceed  to  finish  the  stone  required  to  be  formed,  in  the 
following  order:  first,  by  proceeding  with  the  convex  spherical  surface  ;  secondly, 
the  upper  concave  conical  surface  ;  thirdly  and  lastly,  the  concave  spherical 
surface.  Having  approached  as  nearly  to  the  required  surfaces  as  can  be  done 
with  safety,  the  upper  conical  concave  surface  will  be  reduced  to  its  ultimate 
form  by  cutting  away  the  substance  carefully,  so  that  the  surface  between  the 
two  arris  lines  may  at  last  coincide  with  all  the  points  of  a  straight  edge  applied 
perpendicularly  to  the  two  arrises. 

The  convex  spherical  face  will  be  formed  ultimately  by  cutting  the  substance 
of  the  stone  carefully,  so  that  the  surface  between  the  arris-line  on  the  top,  and 
the  circular  convex  arris-line  on  the  outside  of  the  lower  bed,  may  at  last  agree 
with  all  the  points  of  the  circular  concave  edge  of  the  rule  made  to  a  portion  of 
the  arc  Abed,  Jig.  3,  of  the  section  of  the  dome.  This  circular  edged  rule  must 
be  frequently  applied  ;  and  in  each  application  the  plane  of  the  arc  must  be 
perpendicular  to  the  surface,  gradually  approaching  to  its  required  sphericity. 

To  form  the  concave  surface  of  the  upper  bed  of  the  stone,  reduce  the  solid 
by  carefully  cutting  parts  away,  so  as  at  length  the  surface  between  the  upper 
arris  and  the  intermediate  line  drawn  on  the  inside  formerly  concave,  may  coin- 
cide with  all  the  points  of  a  straight  edge  applied  perpendicularly  to  the  upper 
arris-line  from  any  point  of  this  arris. 

The  concave  spherical  surface  will  be  formed  in  the  same  manner  as  the  con- 
vex spherical  surface  already  supposed  to  be  formed,  with  this  difference,  that 
the  circular  edge  which  proves  the  sphericity,  by  trial  must  be  convex  instead  of 
being  concave.  This  convex  surface  lies  between  the  lower  arris,  terminating 
the  upper  conic  bed,  and  the  inner  arris  of  the  lower  bed. 

As  to  the  lower  bed  it  is  already  formed,  being  part  of  the  plane  surface, 


&B.CTIGN  OF  A  DOIJLKo 


n.u. 


CONSTRUCTION  OF  THE  MOULDS. 


t  IT 


formerly  one  of  the  ends  of  the  hollow  cylinder,  in  a  plane  perpendicular  to  the 
common  axis;  and  as  to  the  ends  forming  the  vertical  joints, they  were  at  first 
formed  in  making  the  hollow  cylindric  solid  ;  so  that  one  of  the  stones  in  the 
lower  course  is  now  finished. 

One  of  the  stones  in  the  second  course  being  first  formed  into  the  frustrum 
of  a  cylindric  wedge,  as  was  done  with  the  stone  formed  for  the  first  course, 
the  several  faces  which  contain  this  solid  are  as  follow  : — grxw,fig.  5,  represents 
the  plane  truncated  sector  forming  the  top,  st  being  the  arris-line  between  the 
spheric  surface  on  the  convex  side  of  st,  and  the  conic  surface  in  the  concave 
side  of  st ;  grr'g',fig.  8,  the  convex  cylindric  surface,  g"rn''  the  arris  between  the 
convex  spheric  and  the  convex  conic  surfaces,  and  r'ggr',  fig.  9,  the  concave 
cylindric  surface ;  x"w",  the  arris  between  the  concave  spheric  surface  under- 
neath and  the  concave  conic  surface  above,  the  arris-line  being  drawn  upon  the 
lower  plane  surface,  we  shall  thus  have  the  arris-lines  between  the  spheric  and 
conic  surfaces. 

The  solid  being  cut  as  before  directed  between  the  arris-lines  until  the  surfaces 
are  duly  formed,  we  shall  have  also  one  of  the  stones  in  the  second  course  com- 
pletely prepared  for  setting. 

Perhaps  for  preparing  the  stones  for  the  first  and  second  courses,  as  also  the 
stones  near  the  summit,  no  better  method  can  be  followed  than  that  which  we 
have  employed  in  preparing  a  stone  in  each  of  the  two  lower  coursts,  yet  as  the 
saving  of  an  expensive  material  and  labor  is  a  desirable  object,  we  shall  here 
show  how  the  waste  of  stone  and  the  labour  of  the  workman  may  in  a  con- 
siderable degree  be  prevented. 

PLATE  XXIV.   ANOTHER  METHOD. 

Let  fig.  1  be  the  section  of  the  dome,  and  fig.  2  a  plan  of  the  same,  showing 
the  convex  side.  Now  as  the  saving  of  material  will  be  principally  in  the  stones 
which  constitute  the  intermediate  courses,  we  shall  select,  for  an  example,  the 
fifth  stone  from  the  bottom  and  from  the  summit.  The  section  of  this  stone  is 
abed,  fig.  1. 

Draw  de  parallel,  and  ae  perpendicular  to  the  base  of  the  dome.  Then  in- 
stead of  first  working  the  sides  of  the  stone,  so  that  the  section  may  be  a  rec- 
tangle, of  which  two  sides  are  parallel  and  two  perpendicular  to  the  horizon  ; 
let  it  be  wrought  into  the  form  abede,  so  that  the  part  de  may  be  parallel  to  the 
horizon. 

Let  the  section  abede  be  transferred  to  No.  1,  at  abede,  and  let  fghi,  No.  1,  be 
the  section  of  the  rough  stone,  out  of  which  the  coursing-stone  of  the  dome  is 
to  be  wrought;  the  sides  of  the  section  of  the  rough  stone  having  two  parallel 
and  two  perpendicular  faces  to  the  lower  bed  of  the  stone.  The  wrought  ston  e 
must  be  selected  sufficiently  large,  so  that,  when  it  is  reduced  to  the  intended 
form,  all  the  spherical  and  conical  surfaces  must  be  entire,  and  thus  the  arrises 
will  also  be  entire. 

The  first  operation  is  to  reduce  the  stone  by  taking  away  a  triangular  prism 
from  the  top  ;  the  section  of  which  prism  is  represented  by  kli,  No.  1,  so  that  the 
surface  of  which  the  section  is  de,  may  be  a  plane  surface. 


118 


OPERATIVE  MASONRY. 


No.  2  is  an  orthographical  projection  of  the  stone,  of  which  the  section  is 

mnop,  after  being  thus  reduced,  grst  representing  the  plane  surface,  <;f  which 
the  section  is  k1,  No.  1,  is  parallel  to  the  plane  of  projection.  On  the  plane  sur- 
face grst,  No.  2,  apply  a  mould  xuvw,  so  that  the  radius  of  the  curved  edge  uv, 
may  be  equal  to  the  line  dx,  fig.  1,  dx,  being  parallel  to-the  base,  meeting  the  axis 
in  x,  and  that  vu  and  wx  may  be  straight  lines  tending  to  the  centre  of  the  arc 
ux ;  and  that  the  chord  of  the  arc-  ux  may  be  equal  to  the  length  of  the  chord  of 
the  upper  arris  of  stone.  Draw  lines  along  xu,  uv,  and  wv,  of  the  mould,  and  let 
vw  be  the  line  drawn  by  the  curved  edge  vw  of  the  mould,  uv  the  line  drawn  by 
the  straight  edge  uv  of  the  mould,  and  xw  the  line  drawn  by  the  straight  edge 
xw  of  the  mould. 

Take  the  mould  away,  and  there  will  remain  the  three  lines  viz.  the  arc  vw, 
and  the  straight  lines  vu  and  wx,  which  radiate  to  the  centre.  Then  vw  is  the 
upper  arris  of  the  stone,  and  the  straight  lines  vu  and  wx,  as  in  the  planes  of  the 
meeting  joints  of  the  two  adjacent  stones  in  the  same  course  to  that  which  is 
now  in  the  act  of  working. 

The  second  operation  is  to  work  the  spherical  surface  by  means  of  the  bevel 
edc,  Jig.  1,  in  such  a  manner,  that  while  the  point  d  is  upon  any  point  of  the  arc 
vw,  No.  2,  the  straight  edge  de  may  coincide  with  the  plane  surface  xuvw,  No.  2, 
and  the  curved  edge  dc  may  coincide  with  the  spherical  surface  required  to  be 
formed,  and^  lastly,  that  the  plane  of  the  bevel  cde  may  be  perpendicular  to  the 
arris  line  vw. 

The  third  operation  is  to  find  the  vertical  joints  of  the  stone  :  these  will  be 
formed  by  means  of  a  common  square,  of  which  the  right  angle  is  contained  by 
two  straight  lines,  so  that  when  the  vertex  of  the  angle  of  the  square  is  upon 
any  point  of  the  line  vw  or  ux,  No.  2,  the  inner  face  of  application  of  the  third 
part  must  be  upon  the  plane  surface  tuvw,  and  the  edge  of  application  of  the 
thin  part  upon  the  vertical  joint,  and  that  both  edges  of  application  may  be  per- 
pendicular to  the  line  vw  or  ux. 

The  fourth  operation  is  to  form  the  conical  upper  bed  of  the  stone  by  means 
of  the  bevel  fgh,  Jig.  1,  so  that  when  this  conic  surface  is  wrought  to  the  re- 
quired form,  and  the  vertex  g  of  the  angle  is  applied  upon  any  point  of  the  curve 
uv,  No.  2,  the  curved  edge  gh  may  then  coincide  with  the  spherical  surface,  and 
the  straight  edge  gf  with  the  conical  bed  thus  formed,  the  edges  gf  and  gh  being 
perpendicular  to  the  arris  ux. 

Thus  four  sides  of  the  stone  are  now  formed,  viz.  the  convex  spherical  surface, 
the  concave  conical  surface,  and  the  two  vertical  joints  of  the  stone.  By  gaug- 
ing the  spherical  surface  to  its  breadth,  the  under  or  convex  conical  surface  may 
be  formed  by  means  of  the  same  bevel  fgh,  fig.  1,  and  gauging  the  sides  of  the 
stone  which  form  the  joints,  viz.  the  concave  and  convex  conic  surfaces  which 
form  the  upper  and  lower  beds,  and  the  two  vertical  joints  from  the  spherical 
convex  surface,  we  shall  now  be  enabled  to  form  the  concave  spherical  surface 
by  means  of  a  slip  of  wood,  of  which  one  edge  is  formed  to  the  curve  of  the 
inside  of  the  section,  No.  1,  and  thus  we  have  formed  a  stone  of  the  fifth  course, 
as  required  to  be  done.  In  the  same  manner  the  stones  of  every  course  may  be 
formed. 


CONSTRUCTION  OF  THE  MOULDS. 


119 


This  method  will  never  require  so  much  stone  as  the  former  or  first  method, 
nor  yet  the  quantity  of  workmanship;  but  it  requires  greater  care  in  the  execu- 
tion. This  last  method  was  used  in  the  construction  of  the  dome  of  the  Hunle- 
rian  Museum  at  Glasgow. 

To  execute  a  vault,  of  which  both  the  extrados  and  intrados  are 
conic  surfaces,  having  a  common  vertical  axis,  the  solid  being 
equally  thick  between  the  conic  surfaces,  so  that  in  the  joint  lines 
those  of  beds  may  be  horizontal,  and  those  of  the  headings  in  ver- 
tical planes  passing  along  the  axis. 

The  easiest  method  of  executing  this,  is  to  form  the  beds  so  that  when  built 
they  will  unite  in  horizontal  planes,  and  the  headings  in  vertical  planes. 

Let  ABC,  Jig.  3,  be  a  section  of  the  exterior  surface,  and  EFG  a  section  of 
the  interior  surface  ;  the  lines  AB  and  EF  being  parallel,  as  also  the  lines  CB. 
and  GF. 

In  order  for  the  easy  application  of  the  bevels,  it  will  be  Convenient  to  worfe 
the  exterior  faces  of  the  stones  first  as  plane  surfaces ;  then  form  the  joints  by 
means  of  a  face  mould,  and  the  angles  which  the  joints  make  with  the  planes  of 
the  faces  by  means  of  the  bevels,  and  lastly,  run  a  draught  upon  each  end  of  the 
face  first  wrought  according  to  the  proper  curve  of  the  cone. 

Let  dSv  be  the  exterior  line  of  the  plan,  D  being  the  centre  of  all  the  circles 
which  form  the  seats  of  the  joint  lines  in  the  plan.  Divide  the  semi-circular  arc 
dSv  into  as  many  equal  parts  as  the  number  of  vertical  joints  in  the  semi-cir- 
cumference. 

Let  there  be  five  stones,  for  instance,  in  each  quadrant  ;  therefore,  if  dS  and 
Sv  be  quadrants,  divide  c?S  into  five  equal  parts,  and  let  de  be  the  first  part. 
Through  the  point  e,  draw  the  radius  fD.  Bisect  the  arc  de  in /,  and  draw  Cf 
a  tangent  to  the  semi-circular  arc  dSv  at  the  point /.  Bisect  each  of  the  arcs 
between  the  points  of  division  in  the  quadrantal  arc  dS,  and  the  tangents  being 
drawn  at  each  point  of  bisection,  will  form  the  polygonal  base  Cfmnopt 

To  form  the  angle  of  the  mitre  at  the  meeting  of  two  heading  joints.  In  Cf 
or  Cf  produced,  take  any  point  g,  and  draw  gh  perpendicular  to  the  diameter 
AC,  meeting  AC  in  the  point  h.  Draw  hi  perpendicular  to  CB,  meeting  CB  in 
the  point  it  In  DC  make  hk  equal  to  hi  and  join  kg ;  then  will  the  angle  ~Dkg 
be  the  bevel  of  the  mitre. 

The  sections  of  each  of  the  stones  as  they  rise*  being  dt'h'G',  t'i'fb'^  i'j'k'f'i  the 
dimensions  of  the  stones  will  be  found  as  follows.  Through  the  points  e', 
draw  the  straight  lines  d'c,  h'g',  k'l't  intersecting  the  inner  line  GF  in  the  points 
V,  /,  k\.  Through  /,  k\  draw  the  lines  ab',  d'f,  h'k\  perpendicular  to  AC* 
Also  through  the  points  e',  i',f,  draw  t'g\  iT,  as  also  Cc,  which  will  complete  the 
sections  of  the  stones.  The  other  side,  AEFB  of  the  section,  exhibits  the  sec- 
tions of  the  stones  perpendicular  to  the  intrados  and  extrados  of  the  lines  ;  the 
sections  of  the  stones  being  AEr,  E.£'r,  @yVt,  and  the  sections  of  the  joints  Er, 
@t,  3/V.  To  find  the  curve  of  the  stone  at  any  section  as  Er  at  the  point  r.  With 
the  horizontal  radius  5r,fg.  3,  and  from  the  centre  5,  describe  an  arcr3.  From 
the  point  3,  draw  32  perpendicular  to  5r,  meeting  or  in  2.  In  2r  make  21  equal 
to  the  nearest  distance  between  the  point  2  and  the  line  AB.  From  some  point 
16 


120 


OPERATIVE  MASONRY. 


found  in  the  line  5r,  describe  an  arc  13,  and  the  arc  13  will  be  the  curvature  of 
the  top  of  the  stone  at  the  joint.    This  is  shown  at  Jig,  4. 

Figs.  5  and  6  exhibit  another  method  of  finding  the  curve  at  the  joint,  by 
means  of  the  radius  of  curvature. 

SECTION  XIII. 

CONSTRUCTION  OF  THE   MOULDS,  AND  FORMATION  OF  THE 
STONES,  FOR  RECTANGULAR  GROUND  VAULTS. 

CONSTRUCTION  OF  GROINED  VAULTS,  CYLINDRETJC  SURFACES. 

A  cylindretic  surface  is  every  surface  which  may  be  generated 
by  a  straight  line  moving  parallel  to  iUelf,  and  intersecting  a  given 
curve  line. 

Since,  in  good  masonry,  the  sides  of  the  joints  of  any  course  of  a 
vault  are  made  to  terminate  upon  the  intrados,  in  a  horizontal  plane 
perpendicularly  to  the  intrados,  if  the  intrados  be  a  cylindric  surface, 
of  which  the  sides  are  straight  lines  parallel  to  the  horizon,  the  sides 
of  the  coursing  joints  will  be  in  planes  intersecting  the  intrados,  per- 
pendicularly in  straight  lines,  and  the  course  will  form  one  prismatic 
solid  ;  hence  all  the  right  sections  will  be  equal  and  similar  figures, 
and  will  be  in  vertical  planes. 

The  stones  of  a  groin,  which  have  any  difficulty  in  their  construc- 
tion, are  those  at  the  meeting  of  two  adjacent  sides,  and  it  is  only 
the  formation  of  these  which  we  shall  describe. 

In  order  to  form  the  stone  of  any  course,  circumscribe  a  rectangle 
round  each  corresponding  right  section  of  the  course,  so  that  the  sides 
of  the  rectangle  may  each  pass  through  the  point  of  meeting  of  every 
two  sides  of  the  section  of  the  course,  and  that  two  of  these  sides  may 
be  parallel,  and  two  perpendicular  to  the  horizon,  as  was  done  in  re- 
spect of  the  execution  of  niches  in  horizontal  courses,  and  in  the 
formation  of  the  stones  of  a  dome. 

In  the  first  place,  the  stone  must  be  squared  in  such  a  manner,  that 
every  two  faces  which  meet  each  other  may  form  a  right  angle,  and 
that  two  of  the  faces  may  be  parallel  and  six  perpendicular  to  the 
horizon,  and  that  only  two  of  the  six  faces  which  are  perpendicular 
to  the  horizon  may  form  a  receding  angle  ;  and,  moreover,  that  the 
figure  of  the  two  faces  which  are  parallel  to  the  horizon  may  be 
formed  to  the  plan  of  the  stone,  as  formed  by  the  rectangular  planes. 

The  two  vertical  faces  which  form  a  right  angle  with  each  other, 
but  which  do  not  join  in  consequence  of  the  two  vertical  faces  which 
form  the  receding  angle  coming  between  them,  are  those  two  faces  in 
the  plane  of  the  vertical  joints. 

The  figures  of  these  faces  must  be  made  to  theA  rectangle,  cir- 
cumscribing each  respective  section. 

The  next  operation  is  to  gauge  two  lines  on  the  upper  level  surface, 
so  as  to  form  the  return  arris  between  the  upper  bed  and  the  con- 


CONSTRUCTION  OF  THE  MOULDS. 


131 


vex  cylindretic  surface  on  each  side  of  the  groin  ;  this  operation  be- 
ing done,  gauge  two  lines  on  the  lower  level  surface,  so  as  to  form 
the  return  arris  between  the  lower  bed  and  the  concave  cylindretic 
surface  on  each  side  of  the  groin.  These  two  lines  will  thus  form  a 
right  angle,  which  being  drawn,  gauge  a  line  upon  each  of  the  ver- 
tical sides  which  form  the  internal  right  angle,  and  thebe  lines  will 
be  the  arris  of  the  stone  on  each  side  of  the  groin  bet  ween  the  upper 
bed  of  the  stone  and  the  concave  cylindretic  surface  ;  and,  lastly, 
gauge  a  line  upon  each  of  the  vertical  surfaces  which  are  opposite  to 
those  forming  the  internal  angle,  so  that  each  of  the  two  lines  thus 
drawn  may  form  the  arrises  between  the  convex  surface  and  the  low- 
er bed. 

The  arrises  of  the  stone  being  thus  drawn,  it  must  be  reduced  to 
such  surfaces,  that  each  of  the  lines  may  be  the  arris  of  every  two 
adjacent  surfaces. 

The  two  beds  of  the  stone  are  plane  surfaces,  and  are  therefore 
formed  by  means  of  a  straight  edge.  The  other  cylindretic  surfaces 
are  brought  to  form  by  means  of  a  curved  edge  made  to  the  place 
where  the  stone  is  to  be  set.  It  is  evident  that  when  the  curve  va- 
ries, a  mould  must  be  made  to  every  stone. 

Fig.  1,  Plate  XXV,  is  the  plan  of  a  ground  vault  with  its  vertical  right  sec- 
tions upon  each  side  of  it.  In  the  plan  A,B,C,D,  exhibit  the  springing  points  of 
the  groins,  AC  anil  BD  are  the  plans  of  the  groins,  or  intersections  of  the  cvl- 
indretic  surfaces.  These  plans  of  the  surfaces  of  the  stones  in  the  intradosi 
which  form  the  ground  angles,  are  exhibited  along  the  lines  AC,  BD. 

IKL  is  a  section  of  the  intrados,  and  pqr  a  section  of  the  extrados,  the  intra- 
dos  and  extrados  being  concentric  semi-circular  arcs;  EFG  and  mno  are  sec- 
tions of  the  intrados  and  extrados  of  the  other  vault,  being  each  a  surbased  semi- 
elliptic  arc,  equal  in  height  respectively  to  the  semi-circular  arcs  of  the  other 
vault. 

These  two  sections  of  each  vault  exhibit  the  section  of  each  course  of  stone, 
with  the  circumscribing  rectangle.  These  stones  are  exhibited  separately  at 
No.  1,  No.  2.  No.  3,  &c. 

No.  1  is  that  over  the  centre  of  the  section  of  the  semi-circular  vault ;  No.  2, 
that  next  to  the  stone  over  the  centre  ;  No.  3,  the  second  stone  from  that  over 
the  centre  ;  and  so  on. 

No.  1,  A,  is  a  section  of  the  course,  or  of  a  stone  over  the  centre  of  one  of  the 
semi-circular  branches  of  the  groined  vault,  showing  the  circumscribing  rectan- 
gle ;  and  No.  1,  B,  is  the  underside  of  the  same  stone,  forming  a  part  of  the  in- 
trados of  the  vault.  This  exhibits  the  stone  as  if  squared  with  the  portions  of 
the  plans  of  the  groins,  which  are  to  be  wrought  on  this  stone,  as  also  the  plans 
of  the  intersections  of  the  joints  with  the  upper  surface  or  intrados. 

Having  wrought  a  concave  draught  along  the  lines  ab,  cd  to  the  middle  of  the 
intrados  EFG  of  the  section  of  the  elliptic  vault,  the  intermediate  surface  be- 
tween ab  and  erf  maybe  formed  by  means  of  a  straight  edge  applied  parallel 
to  ac  or  bdy  and  having  wrought  the  concave  draught  along  the  lines  ef  gh,  so 
that  the  points  c,  /,  g,  h  may  remain,  while  the  intermediate  is  sunk,  and  so 


122 


OPERATIVE  MASONRY. 


that  the  draught  thus  sunk,  may  have  the  same  curve  as  the  intrados  line  IKL 
of  the  semi-circular  branch.  The  intermediate  part  may  be  formed  by  means  Oi 
a  straight  edge  applied  parallel  to  egorfh,  and  thus  the  two  cylindretic  surfaces 
crossing  each  other  will  form  the  groins  ik,  Im,  which  belong  to  the  central 
stone,  and  which  are  a  portion  of  the  whole  groins  resting  on  the  springing 
points. 

These  arrises  being  formed  by  the  intersection  of  the  cylindretic  surfaces, 
•which  meet  each  other  at  very  obtuse  angles,  ought  to  be  done  with  care,  other- 
wise the  beauty  of  the  intersections  would  be  destroyed. 

No.  2,  3,  &c.  require  a  similar  description  to  that  of  No.  1,  and  therefore  wilj 
be  sufficiently  understood  from  that  now  given. 

P  and  Q  exhibit  the  manner  of  forming  one  of  the  stones  agreeable  to  the 
section  of  one  of  the  elliptic  branches  of  the  groined  vault  after  having  squared 
the  stone,  this  stone  being  supposed  to  be  the  second  from  that  over  the  centre. 

It  is  worthy  of  notice,  that  except  the  stone  in  the  summit  of  the  groined 
vault,  any  four  stones  equally  distant  from  the  centre  of  the  ground  ceiling, 
though  reduced  by  the  same  moulds  to  the  same  number  of  similar  surfaces, 
and  though  every  two  corresponding  similar  surfaces  meet  each  other;  yet  nev- 
ertheless any  one  of  the  four  stones  can  only  fit  one  of  the  four  situations  ;  so 
that  the  same  moulds  will  serve  for  the  formation  of  four  stones  equally  distant 
from  the  summit. 


SECTION  XIV. 

THE  MANNER  OF  FINDING  THE   SECTIONS  OF  RAKING 

MOULDINGS. 

To  find  the  raking  mouldings  of  a  canted  bow-window,  with 
munions  and  transoms. 

Let  the  plan  of  the  window  be  Jig.  1,  Piatt  XVI,  consisting  of  three  sides,  the 
middle  one  being  parallel  to  the  walls,  and  the  other  two  at  an  angle  of  135  de- 
grees each,  with  the  middle  face  of  the  window. 

Also,  let  raQ,Jig.  2,  be  a  horizontal  section  of  one  of  the  angles,  No.  1  being 
a  right  section  of  one  of  the  munions,  the  same  as  the  right  section  of  the  tran- 
som sill  or  lintel,  and  let  ar,  No.  2,  be  the  line  of  mitre  corresponding  to  AR, 
No.  ],  AR  being  perpendicular  to  aQ. 

In  order  to  find  the  right  section,  No.  2,  of  the  angular  munion.  In  the  curves 
of  the  given  section,  No.  1,  draw  lines  through  a  sufficient  number  of  points 
perpendicular  to  aQ,  and  draw  ac  perpendicular  to  ar ;  transfer  the  points  B  C 
from  A,  No.  1,  made  by  the  perpendiculars  to  No.  2;  from  a  to  c  upon  ac,  and 
from  a  to  6  through  the  points  in  ac  draw  lines  parallel  to  ar,  to  intersect  the 
corresponding  lines  parallel  to  Qa  from  the  assumed  points  K,  L,  M,  N,  in  the 
curves,  No.  1,  and  through  these  points  trace  the  curves  which  will  form  one 
side  of  the  section,  No.  2;  repeat  the  same  operation  on  the  other  side,  and  we 
ahall  have  the  complete  section  required. 


OF  A  LINTEL,  OR  AN  ARCHITRAVE. 


123 


Figs.  3  and  4,  No.  1,  is  the  right  section  of  the  raking  moulding  on  a  pedi- 
ment, which  if  supposed  to  be  given,  the  section  No.  2  may  be  found  as  that  at 
No.  2,  from  No.  ],fig>  2;  but  in  this  case  No.  2  is  generally  that  which  is  given, 
and  the  section  No.  1  is  traced  therefrom. 

In  all  these  cases  of  raking  mouldings,  draw  ac  perpendicular  to  ar  the  line 
of  mitre.  To  find  any  point  m,  take  the  point  M  in  the  section  No.  1,  and 
draw  MB  perpendicular  to  AC,  Nos.  1  and  2,  meeting  AC  in  B,  and  draw  Mm 
parallel  to  Rr.  Make  ab  equal  to  AB,  and  draw  bm  parallel  to  ctj,  and  m  will 
be  a  point  in  the  curve.  In  the  same  manner  will  be  found  the  points  j,  k,  l,n, 
No.  2,  from  the  points  J,  K.  L,  N,  No.  1 ;  and  hence  the  section  No.  2  may  be 
traced  from  No.  1. 

Fig.  4  is  described  in  the  same  manner  as  fig.  3. 


SECTION  XV. 

CONSTRUCTION  OF  A  LINTEL,  OR  AN  ARCHITRAVE,  IN  THREE 
OR  MORE  PARTS,  OVER  AN  OPENING,  AND  THE  STEPS 
OF  A  STAIR  OVER  AN  AREA. 

On  the  method  of  building  a  lintel,  or  architrave,  with  several 
stones,  so  that  the  soffit  and  top  of  the  lintel,  or  architrave  may  be 
level  ;  and  that  the  connecting  joints  of  the  course  may  appear  to  be 
vertical  in  the  front  and  rear  of  the  lintel,  or  architrave. 

A  lintel,  or  architrave,  is  frequently  formed  in  several  stones,  from 
the  difficulty  of  procuring  one  of  sufficient  length.  The  method  of 
doing  this  is  founded  upon  the  principle  of  arching,  the  arch  being 
concealed  within  the  thickness  of  the  stones. 

Fig.  1,  Plate  XXVII,  represents  the  upper  part  of  an  aperture,  linteled  as 
specified  in  the  contents  of  this  chapter  ;  the  centre  of  the  radiating  joints  being 
the  vertex  of  an  equilateral  triangle. 

Fig.  2  represents  the  top  of  the  lintel,  exhibiting*  the  thickness  of  the  radia- 
ting joints,  and  the  thickness  of  the  square  joints  on  each  side  of  the  concealed 
arch. 

Fig.  3  represents  the  soffit  of  the  lintel,  exhibiting  the  joint  lines  perpendicular 
to  the  two  edges,  as  the  radiating  as  well  as  the  vertical  joints,  all  terminate  in 
these  lines. 

No.  1  exhibits  the  first  abutment-stone  over  the  pier  ;  No.  2,  the  first  stone  of 
the  lintel ;  No.  3,  the  second  stone,  which  forms  the  key  ;  the  two  remaining 
stones  are  the  same  as  the  first  stone  of  the  lintel,  and  the  abutment-stone  being 
placed  in  reverse  order. 

The  three  stones  here  exhibited,  show  the  manner  of  indenting  the  stones  so 
as  to  form  a  series  of  wedges ;  and  in  order  to  regulate  the  soffit,  the  radiations 
are  stopped  at  half  their  height. 

Fig.  1,  Plate  XXVIII,  exhibits  the  method  of  constructing  an  architrave  over 
columns  when  the  stone  is  not  of  sufficient  length  to  reach  the  two  columns.  No. 
X,  Plan  of  the  upper  horizontal  side  of  the  architrave  exhibiting  a  chain-bar  of 


124 


OPERATIVE  MASONRY. 


wrought-iron,  with  collars  let  in  flush  with  the  top  bed,  the  sockets  being  filled 
with  melted  lead  round  the  collars. 

In  the  plan  and  elevation,  the  same  letters  express  different  sides  of  the  same 
parts  ;  thus  in  the  elevation,^.  1,  the  letter  A  is  written  upon  the  part  express- 
ing the  vertical  face  of  the  stone,  over  the  angular  column  ;  and  A  on  the  plan 
No.  ],  expresses  the  horizontal  side  or  bed  of  the  same  stone.  The  letter  B,  on 
the  elevation  fig.  1,  represents  the  vertical  face  of  the  middle  stone  of  the  archi- 
trave ;  and  B,  on  the  plan,  represents  the  bed  of  the  middle  stone.  The  letter 
C,  on  the  elevation,  represents  the  vertical  face  of  the  stone  over  the  second 
column  ;  and  C  represents  the  upper  horizontal  surface  or  bed.  The  stones  A 
and  C  serve  as  abutments  to  the  middle  stone  B,  which  is  let  in  in  the  manner 
of  a  keystone,  and  therefore  acts  as  a  wedge.  In  order  to  lessen  the  effect  of 
the  pressure  of  the  inclined  sides  from  forcing  the  columns  to  a  greater  distance, 
the  joint  onnmm  has  two  horizontal  ledges,  nn,  mm,  which  will  prevent  the  middle 
part  from  descending. 

D  exhibits  a  stone  in  the  act  of  setting,  and  is  let  down  by  means  of  a  lewis  ; 
a  brick  arch  is  exhibited  over  the  architrave,  in  order  to  discharge  the  weight 
from  above,  and  is  resisted  by  the  abutments  at  the  ends.  The  lateral  pressure 
of  the  brick  arch,  and  of  the  stone  B,  is  entirely  counteracted  by  means  of  the 
chain-bar,  of  which  the  top  is  represented  in  No.  1. 

No.  3,  exhibits  a  section  of  the  work,  z  being  a  section  of  the  arch  in  the 
middle,  and  y  shows  the  void  between.  The  right  section  through  the  middle 
of  the  arch  between  the  columns,  is  the  same  as  shown  at  yz. 

No.  2,  exhibits  the  manner  of  cutting  the  joints  of  the  stones  over  the  column 
g  and  w,  being  the  steps  of  the  socket  and  uuu  the  square  part  of  the  joint. 

On  the  construction  of  stairs  over  an  area  to  an  entrance  door. 

Stairs  of  this  description,  which  consist  of  one  flight,  must  either 
be  supported  upon  a  solid  foundation  raised  from  the  ground  ;  or, 
if  over  a  hollow,  the  steps  must  be  supported  upon  a  brick  arch, 
or  otherwise,  by  working  the  soffits  in  the  form  of  a  concave  curve. 

FF,  represents  the  abutments  of  the  columns;  E,  the  steps  ;  G,  the  cantae  as 
projecting  from  the  wall,  to  support  the  architrave-stone  D. 

Since  the  joints  should  always  be  perpendicular  to  the  curve, 
they  must  all  tend  to  the  centre  of  the  circle  which  forms  the  soffit  ; 
and  since  the  steps  should  rest  firmly  upon  one  another,  they  ought 
to  rest  upon  a  horizontal  surface.  To  accomplish  these  ends,  every 
joint  between  two  steps  ought  to  consist  of  two  surfaces,  one  hori- 
zontal, and  the  other  part  a  plane,  radiating  to  the  axis  of  the  cylin- 
der, of  which  the  soffit  of  the  steps  is  the  curved  surface. 

Fig.  2,  Plate  XXIX,  is  the  plan  ;  Jig.  1,  the  elevation  of  a  semi-circular  arched 
door-way,  built  of  wrought  stone  with  steps,  and  fig.  3,  a  section  of  the  same  ; 
ab  is  the  curve-line,  representing  a  section  of  the  soffits.  The  joints  are  here 
drawn  to  the  centre  c  of  the  arc  ab. 

In  this  case,  where  there  are  no  brick  arches  below,  the  joints  should  be  plug- 
ged. Fig.  4  exhibits  a  section  of  the  steps,  showing  the  plugs,  one  in  each  end 
perpendicular  to  the  surface  of  the  joint. 


Tl.  29. 


Tl.  30. 


CONSTRUCTION  OF  STONES  FOR  GOTHIC  VAULTS.  125 


SECTION  XVI. 

CONSTRUCTION   OF    THE  STONES  FOR  GOTHIC  VAULTS,  IN 
RECTANGULAR  COMPARTMENTS  UPON  THE  PLAN. 

GROINED  ARCHES  SPRINGING  FROM  POLYGONAL  PILLARS. 

To  execute  a  ribbed-groined  ceiling  in  severies,  upon  a  rectangu- 
lar plan,  so  that  the  ribs  may  spring  from  points  in  the  quadrantal 
arc  of  a  circle,  of  which  the  centres  are  in  the  angular  points  of  the 
plan,  and  to  terminate  in  a  horizontal  ridge  parallel  to  the  sides 
of  the  severies,  and  in  a  vertical  plane,  bisecting  each  side  of  the 
plan. 

Let  STVW,  Plate  XXX,  fig.  1,  be  a  portion  of  the  plan  consisting  of  two 
severies  STUX,  XUVVV,  the  points  S,  T,  U,  V,  W,  X,  being  the  points  into  which 
the  axis  of  the  pillars  are  projected. 

Bisect  VW  by  the  perpendicular  rL,  and  bisect  VU  by  the  perpendicular  ph. 
Draw  the  straight  lines  uq,  vh,  wm,  xn,  yo,  radiating  from  V  to  meet  the  ridge 
lines  rL  and  hp  in  the  points  r,  q,  L,  m,  n,  o,  and  the  arc  tz  described  from  v  in 
the  points  u,  v,  w,  x,y,  and  these  lines  will  be  the  plans  of  the  ribs  for  one  quarter 
of  a  severy. 

Suppose  now  the  rib  over  tr  to  be  given,  and  let  this  rib  be  Jig.  2,  which  is 
here  made  double.  The  half  abc  is  the  rib  which  stands  upon  r  t,  the  curve  be, 
Jig.  2,  and  the  plans  tr,  uq,  vh,  wm,  xn,  yo,  zp,  fig.  1,  of  the  ribs  are  given  by  the 
architect  in  the  plan  and  sections  of  the  work  :  it  is  the  workman's  province  to 
find  the  curvature  of  the  ribs,  and  the  formation  of  the  stones  for  the  ceiling. 

For  this  purpose  we  shall  suppose  that  the  chords  which  are  formed  by  the 
joints  in  the  intrados  upon  the  meeting  of  the  rib  over  tr  to  be  equal ;  therefore 
divide  the  curve  be,  Jig.  2,  into  equal  parts,  so  as  to  admit  of  vault  stones  of  a 
convenient  size. 

From  the  points  1,  2,  3,  &c.fig.  2,  in  the  arc  6c,  draw  lines  perpendicular  to  ab 
the  base  of  the  rib.  Transfer  the  parts  of  the  line  ab  to  rt,  fig.  1,  and  let  A  be 
one  of  the  points  representing  e,  Jig.  f^LIn  fig-  L,  draw  ut  and  produce  ut,  and 
Lr  to  meet  each  other  in  the  point  3.  Draw  the  straight  line  AB  radiating  to 
the  point  2,  to  meet  the  plan  uq  in  B.  Join  uv  and  produce  vu,  and  Lr  to  meet 
in  3,  and  draw  the  straight  line  BC  radiating  from  2,  to  meet  the  plan  vh  in  C. 
Join  vw,  and  produce  vw  and  hp  to  meet  each  other  in  H.  Draw  CD  radiating 
to  the  point  H,  to  meet  wm  in  D.  Join  wx  and  produce  ivx,  and  hp  to  meet  each 
other  in  I,  and  draw  DE  radiating  to  the  point  I,  to  meet  xn  in  E.  Find  the 
points  F  and  G  in  the  same  manner  as  each  of  the  points  B,  C,  D,  E,  have  been 
found,  and  the  compound  line  ABCDEFG  will  be  the  line  of  joints  correspond- 
ing to  the  point  5,  fig.  2.  Find  the  lines  corresponding  to  the  other  joints  in  the 
same  manner.  Transfer  the  divisions  in  the  line  uq  to  the  base  line  of  Jig.  3, 
and  draw  lines  perpendicular  to  the  base  as  ordinates.    Transfer  the  ordinates 


126 


OPERATIVE  MASONRY. 


of  Jig.  2  to  their  corresponding  ordinate  in  Jig.  3,  and  draw  the  curves  which  will 
complete  the  inner  edge  of  the  rib,  Jig.  3.  In  the  same  manner  find  the  cuive 
of  the  ribs,  Jigs.  4,  5,  6,  &c.  which  stand  over  the  lines  vh,  wm,  xn,  &c. 

Fig.  7  exhibits  apart  of  the  plan  of  a  groin-ceiling,  consisting  of  two  severies 
when  the  plans  of  the  piers  are  squares,  of  which  the  angular  points  terminate  in 
the  sides  of  the  plan  of  each  severy,  and  then  we  have  only  to  find  the  diagonal 
ribs  and  those  upon  the  narrow  side  of  the  severy.  It  must,  however,  be  ob- 
served, both  in  Jigs.  1  and  7,  that  only  one  of  the  curves  which  belong  to  arches 
of  the  two  sides  of  a  severy  can  be  given,  the  other  must  be  found  in  the  same 
manner  as  the  curves  of  the  intermediate  ribs.  In  Jig.  7  the  plan  of  the  joints 
has  only  two  points  of  convergence,  which  are  found  by  producing  the  side  of 
the  square  which  forms  the  plan  of  the  pillars,  and  the  plan  of  the  ridge-lines, 
till  they  meet  each  other. 

We  shall  now  proceed  towards  the  formation  of  the  stones  of 
the  vaulting. 

Plate  XXXI.  Fig.  I.  Let  A  BCD  be  the  plan  of  one  quarter  of  a  severy,  and  let  hC 
and  if  be  the  seats  of  two  adjacent  ribs,  and  let  hyjNC  be  the  rib  which  stands 
upon  hC,  and  let  klmn  be  the  plan  of  the  soffit  of  a  stone.  Perpendicular  to  hC 
draw  ky  and  Ij,  and  draw  yg  parallel  to  hC.  Produce  nk  to  s  and  nm  to  o.  Draw  lo 
and  Is  respectively  parallel  to  sn  and  nm.  Draw  Ir  perpendicular  to  Is  ;  make  Ir 
equal  to  gj,  and  join  sr.  Draw  lu  perpendicular  to  sn  ;  and  from  s,  with  the  radius 
sr,  describe  an  arc  meeting  lu  in  the  point  u.  Draw  uv  and  nv respectively  par- 
allel to  sn  and  su.  Perpendicular  to  no  draw  oq  and  mp.  Make  oq  and  mp  each 
equal  to  gj,  and  join  np  and  nq.  Draw  pt  perpendicular  to  nq,  meeting  nq  in  the 
point  t.  To  form  the  winding  surface  of  the  intrados,  first  work  the  soffit  as 
a  plane  surface  ;  on  the  plane  surface  describe  the  Jigs.  usnv.  Make  nw  equal 
to  nt. 

In  Jig.  2  make  the  angle  abc  equal  to  sno,  fg.  1,  and  make  the  angle  cbe,  Jig.  2, 
equal  to  onq.  Having  the  two  legs  cba,  cbe  of  a  right-angled  trehedral,  find 
the  angle  ghi,  which  the  hypothenuse  makes  with  the  leg  cbe.  Secondly,  form 
the  bed  of  the  stone  to  make  an  angle  at  the  arris-line  nv  with  the  surface 
usnv,  equal  to  the  angle  ghi,  Jig.  2.  Draw  wx  upon  the  end  of  the  stone  thus 
formed  perpendicular  to  nw,  and  make  wx  equal  to  tp,  and  on  the  end  of  the 
stone  draw  nx.  Join  ku;  then  the  four  points  n,  k,  u,  x,  are  the  four  angular 
points  of  rhe  soffit  of  the  stone.  The  other  end  of  the  stone  will  .be  formed 
in  a  similar  manner. 

On  the  nature  and  construction  of  Gothic  ceilings. 

Let  A,  B,  C,  D,  Plate  XXXII,  be  the  springing  points,  AC  and  BD  the  plans 
of  the  groins  disposed  in  the  vertices  of  the  angle  of  a  rectangle,  their  plans 
bisecting  each  other  in  the  point  e;  also  let  QJJ  and  SX,  passing  through  the 
point  e,  and  bisecting  the  angles  AeB,  BeC,  CeD,  DeA,  be  the  plans  of  the  ridges 
of  the  gothic  arches,  and  let  AE,  AH,  BJ,  BK,  CM,CN,  DP,  DG,be  the  spring- 
ing lines  of  the  gothic  ceiling. 

Moreover,  let  the  four  straight  lines  EG,  HJ,  KM,NP,  at  right  angles  to  QU 
and  SX,  be  the  plans  of  four  right  sections  to  each  wing  of  the  groined  vault ; 


3  i 


G O TM I C   AM.  CUE 8  > 


PI.  3.3. 


CONSTRUCTION  OF  STONES  FOR  GOTHIC  VAULTS.  127 


From  the  point  k,  as  a  centre  with  the  radius  kp,  describe  the  arc  hg ;  and 
and  let  the  springing-lines  AE,  DG,  AH,  JB,  &c.be  such  as  to  meet  respectively 
in  the  points  Q,  S,  &c. 

To  construct  the  ribs  which  are  at  right  angles  to  the  ridge-lines,  and  of  which 
their  plans  are  EG,  HJ,  &c.  Let  us  suppose  that  the  given  rib  is  EFG,  standing 
upon  EG  as  its  plan.  Prolong  AE  and  DG  to  meet  each  other  in  the  point  Q. 
Divide  the  half  curve  EF  of  the  arch  into  as  many  equal  parts  as  the  number  of 
courses  is  intended  to  be  in  the  ceiling  on  each  side  of  the  ridge-line  of  the  in- 
trados  of  the  arch  ;  let  us  suppose  that  this  number  is  six,  and  that  h  is  the  first 
point  of  division  from  the  bottom  point  E  of  the  rib,  the  succession  of  parts 
being  Eh,  hi,  &c.  From  the  points  h,  i,  &c.  draw  the  straight  lines  hp,  iq,  &c. 
perpendicularly  to  EG,  meeting  EG  in  the  points  p,  q,  &c.  Through  the  joints 
p,  q,  &c.  draw  from  the  point  Q,  the  lines  Q,r,  Qs,  &c,  meeting  AC,  the  plan  of 
the  groin  in  the  points  r,  s,  &c,  and  perpendicularly  to  AC  draw  the  straight 
lines  rj,  sk,  &c.  Make  rj,  sk,  &c,  each  respectively  equal  to  ph,  qi,  &C.  through 
the  points  A,  /,  k,  &c,  draw  the  curve  AjkV  for  one  half  of  the  curve  of  the 
groin  rib,  the  other  half  is  symmetrical,  and  therefore  the  same  curve  in  a  re- 
versed order. 

To  find  the  rib  HIJ.  Prolong  AH  and  BJ  to  meet  each  other  in  the  point  S, 
and  draw  the  lines  rS,  sS,  &c.  intersecting  HJ  in  the  points  t,  u,  &c.  Draw  in, 
uo,  &c.  perpendicular  to  HJ,  and  make  tn,  uo,  &c.  respectively  equal  to  ph,  qi,  &c. 
Through  the  points  H,  n,  o,  &c.  draw  the  curve  HI,  and  HI  will  be  the  curve  of 
one-half  of  the  arch  over  the  line  HJ  for  the  plan. 

Hence  we  see  that  the  lines  jh,  ki,  &c.  prolonged  will  meet  the  line  QR  per- 
pendicular to  the  plane  ABCD  in  the  points/,  g,  &e.  at  the  same  heights  Qf,  Qg, 
&c.  as  ph,  pi,  &c.  of  the  heights  of  the  ordinates  of  the  given  rib.  Since  both 
sides  are  symmetrical,  one  description  will  serve  each  of  them. 

To  describe  a  gothic  isosceles  arch  to  any  width,  height,  and  to  a 
given  verticle  angle. 

Plate  XXXIII.  Let  AB,  Jig.  1,  be  the  span  or  width  of  the  arch ;  mC,  perpendicu- 
lar to  AB,  from  the  middle  point  m,  the  height ;  and  eCf  the  vertical  angle  given 
by  the  tangents  Ce  and  Cf,  making  equal  angles  with  the  line  of  height  mC. 

In  this  example,  the  points  e  and /  the  lower  extremities  of  the  tangents,  are 
regulated  by  erecting  Ae  and  Bf,  each  perpendicular  to  AB,  and  making  each 
equal  to  3-4  of  the  height  line,  mC. 

From  the  point  A,  towards  B,  make  Ak  equal  to  Ac  or  Bf,  that  is  equal  to  3-4 
mC  ;  and  from  the  point  C,  the  vertex  of  the  arch,  draw  C^ perpendicular  to  Ci£/ 
In  Ci  take  CI,  equal  to  A&,  and  join  kl;  bisect  kl  by  a  perpendicular,  di  meeting 
Ci  in  the  point  i ;  join  ik,  and  produce  ik  to  g. 

From  the  point  i,  with  the  radius  iC,  describe  an  arc  Cg,  meeting  the  line  ig 
in  the  point  g,  and  from  the  point  k,  with  the  radius  kg,  describe  an  arch  gA, 
and  AgC  will  be  the  one  half  of  the  intrados  of  the  gothic  arch  required. 

Produce  Cm  to  meet  ki  in  the  point  n,  and  in  AB  make  mu  equal  to  mk,  join 
nu,  and  prolong  nu  to  t,  and  un  to  o.  Make  no  equal  to  ni.  From  the  centre  o, 
with  the  radius  oC,  describe  the  arc  Ch,  meeting  ut  in  the  point  h,  and  from  u, 
with  the  radius  uh,  describe  the  arc  MB,  and  BhC  will  be  the  other  half  of  the 
intrados. 

17 


128 


OPERATIVE  MASONRY. 


Upon  AB,  prolonged  both  ways  to  p  and  s,  make  Ap  and  Bs  each  equal  to  the 
length  of  each  one  of  the  arch-stones  in  a  direction  of  a  radius. 

From  the  point  k,  as  a  centre  with  the  radius  kp,  describe  the  arc  pg,  and 
from  the  point  i,  with  the  radius  ig,  describe  the  arc  gr,  and  pgr  will  be  half  of 
the  extrados  of  the  arch. 

In  the  same  manner  will  be  formed  str,  the  other  half  of  the  extrados.  The 
arch-stones  are  divided  upon  the  dotted  line  in  the  middle  into  equal  parts,  and 
the  point  lines  are  drawn  by  the  centres  of  the  intrados  and  extrados  of  the 
arch. 

REMARK. 

When  the  height  of  the  arch  is  equal  to,  or  greater  than  half  the 
span,  and  when  it  is  not  necessary  that  the  vertical  angle  should  be 
given,  the  curves  of  the  intrados  and  extrados  on  the  one  side  may 
be  described  from  the  same  centre,  as  also  those  of  the  other  side 
from  another  centre. 

The  most  easy  gothic  arch  to  describe,  is  that  of  which  the  height  of  the  in- 
trados is  such  as  to  be  the  perpendicular  of  an  equilateral  triangle,  described 
upon  the  spanning  line  as  a  base,  such  is  Jig.  2,  and  these  centres  are  the  points 
to  which  the  radiating  joints  must  tend. 

Gothic  arches  seldom  exceed  in  height  the  perpendicular  of  the  equilateral 
triangle  inscribed  in  the  intrados  of  the  aperture ;  but  when  the  arch  is  sur- 
mounted, and  the  height  less  than  the  perpendicular  of  the  equilateral  triangle 
made  upon  the  base,  draw  a  straight  line  from  one  extremity  of  the  base  to  the 
vertex,  and  bisect  this  line  by  a  perpendicular.  From  the  point  where  the  per- 
pendicular meets  the  base  of  the  arch,  and  with  a  radius  equal  to  the  distance 
between  this  point  and  the  extremity  of  the  base  joined  to  the  vertex,  describe 
an  arc  between  the  two  points,  joined  by  the  straight  line,  and  the  curve  which 
forms  one  side  of  the  intrados  will  be  complete.  In  the  same  manner  will  be 
formed  the  curve  on  the  other  side,  See  Jig.  3,  so  that  by  only  two  centres  the 
whole  of  the  intrados  will  be  formed. 

Fig.  4  and  5  shew  the  method  of  erecting  another  form  of  gothic  arches. 

Fig.  4,  represents  the  manner  of  inserting  the  stone  in  a  straight  wall,  so  as 
to  form  a  circular  pointed  arch. 

Fig.  5,  shows  the  manner  of  forming  the  same  arch.  Let  BC  be  the  base 
line  of  the  arch  ;  find  the  centre  A,  of  BC;  at  A  erect  the  perpendicular  AD, 
the  intended  height  of  the  arch  ;  find  i  the  centre  of  AD,  produce  AD,  to  a  and 
make  Act  equal  to  Ai ;  join  BD,  and  divide  it  into  five  equal  parts  at  1,  2,  3,  4,  5. 
Draw  the  line  a  2  through  the  point  e,  produce  a  2  to  g,  make  g  2  equal  to  a  2, 
and  e  and  g  will  be  the  radiating  points.  From  the  point  c  with  the  radius  eB 
describe  the  arc  B2,  and  from  the  point  g  with  the  radius  g\D,  describe  the  arc 
D2,  and  B2  will  be  the  intrados  of  one  portion  of  the  arch,  and  D2,the  extrados 
of  the  other  corresponding  portion  of  the  arch.  The  extrados  and  intrados  of 
the  remaining  side  may  be  found  in  the  same  manner. 


CHAPTER  V. 


SECTION  I. 

The  ancients  used  several  kinds  of  walls,  in  which  more  or  less 
masonry  was  always  introduced.  They  had  their  incertain,  or  in- 
serted walls — and  also  their  reticulated  walls. 

The  uncertain  or  irregular  walls  are  those  where  the  stones  are 
laid  with  their  natural  dimensions,  and  their  figure  and  size  of 
course  uncertain.  Plate  34,  jig.  1.  The  materials  rest  firmly  one 
upon  another,  and  are  interwoven  together,  so  that  they  are  much 
stronger,  than  the  reticulated,  though  not  so  handsome.  In  this 
kind  of  wall,  the  courses  were  always  level ;  but  the  upright  joints 
were  not  ranged  regularly  or  perpendicularly  to  each  other  in  alter- 
nate courses,  nor  in  any  other  respect  correspondently  ;  but  uncer- 
tainly according  to  the  size  of  the  bricks  or  stones  employed.  Thus 
our  bricks  are  arranged  in  ordinary  walls  in  which  all  that  is  re- 
garded is,  that  the  upright  joints,  in  two  adjoining  courses,  do  not 
coincide.  Walls,  of  both  sorts,  are  formed  of  very  small  pieces,  that 
they  may  have  a  sufficient  of,  or  be  saturated  with  mortar,  which 
adds  greatly  to  their  solidity. 

To  saturate,  or  fill  up  a  wall  with  mortar,  is  a  practice  which 
ought  to  be  had  recourse  to  in  every  case,  where  small  stones,  or 
bricks,  admit  of  it.  It  consists  in  mixing  fresh  lime  with  water,  and 
pouring  it,  while  hot,  among  the  masonry  in  the  body  of  the  wall. 

The  walls  called  by  the  Greeks  Isidomum^fig.  4,  are  those  in  which 
all  the  courses  are  of  equal  thickness  ;  and  Pseudo-isidomum,  or 
false,  fig.  3,  when  the  courses  are  unequal.  Both  these  walls  are 
firm,  in  proportion  to  the  compactness  of  the  mass,  and  the  solid  na- 
ture of  the  stones,  so  that  they  do  not  absorb  the  moistness  of  the 
mortar  ;  and  being  situated  in  regular  and  level  courses,  the  mortar 
is  prevented  from  falling,  and  thus  the  whole  thickness  of  the  wall  is 
united.  In  the  wall  called  complecton,  fig.  2,  the  faces  of  the  stones 
are  smooth  ;  the  other  sides  being  left  as  they  came  from  the  quarry, 
and  are  secured  with  alternate  joints  and  mortar,  the  face  of  this 
wall  was  often  covered  with  a  coat  of  plaster.  This  kind  of  building 
called  Diamixton,  Jig.  5,  admits  of  great  expedition,  as  the  artificer 
can  easily  raise  a  case  or  shell  for  the  two  faces  of  the  work,  and  fill 
the  intermediate  space  with  rubble-work  and  mortar.  Walls  of  this 
kind,  consequently,  consist  of  three  coats  ;  two  being  the  faces  and 


130 


OPERATIVE  MASONRY. 


one  the  rubble  core,  which  is  the  middle  ;  but  the  great  works  of  the 
Greeks  were  not  thus  built.,  for  in  them,  the  whole  intermediate  space 
between  the  two  faces,  was  constructed  in  the  same  manner  as  the 
faces  themselves  :  and  they  besides  occasionally  introduced  diatonos, 
or  single  pieces,  extending  from  one  face  to  the  other,  to  strengthen 
and  bind  the  wall,  fig.  5.  a  a.  These  different  methods  of  uniting  the 
several  parts  of  the  masonry  of  a  wall,  should  be  well  considered  by 
all  persons,  who  are  entrusted  with  works  requiring  great  strength 
and  durability. 

If  the  walls  are  Isidomoi,  and  fastened  together  with  iron,  they  are 
properly  called  cramped,  fig.  5.  c.  c.  c.  The  net-work  structure,  fig.  6, 
was  much  used  in  ancient  Rome,  and  is  beautiful  to  the  sight,  but  is 
liable  to  crack,  wherefore  no  ancient  specimens  of  this  kind  remain. 

Plate  XXXV.  fig.  1,  exhibits  a  species  of  ancient  walls  which  may  be 
seen  at  Naples.  There  are  two  walls  A.  A.  of  square  stones,  four 
feet  thick  ;  their  distance  six  feet.  They  are  bound  together  by  the 
transverse  walls  B.  B.  at  the  same  distance.  The  cavity  C  C.  left  be- 
tween, is  six  feet  square,  and  is  filled  up  with  rubble  stones  and  earth. 

Fig.  2  represents  a  second  kind,  built  of  square  stones,  this  was 
called  Pseudisodomum  D  D  ;  to  be  seen  now  at  Rome  in  the  temple  of 
Augustus.  The  third  species  is  the  uncertain,  Jig.  3  ;  a  specimen  of 
which  still  remains  at  Palestrina,  twenty  miles  east  of  Rome.  Another 
kind,  fig.  4,  which  may  be  seen  at  Sirmion  upon  the  lake  of  Garda,  is 
a  species  of  wooden  walls,  E  E,  and  are  called  Formae  ;  they  are 
stuffed  with  stone  mortar,  &c.  at  random.  The  planks  being  taken 
away  the  wall  F  E.  appears  ;  and  is  called  formaceous. 

The  fifth  kind,  fig.  5,  are  walls  made  of  cement,  G  G.  composed  of 
rough  pebbles  out  of  a  river  or  from  a  rock  ;  sometimes  of  shell,  as 
are  the  walls  of  Turin  in  Piedmont.  This  kind  of  wall  should  be 
bound  by  three  courses  of  bricks,  at  the  height  of  two  feet,  as  H.H. 

The  sixth  kind  is  brick-work  ;  fig.  6,  which  especially  in  the  walls 
of  a  city,  or  extraordinary  building,  is  constructed  like  the  Diamix- 
ton,  for  the  bricks  appear,  I.  I,  and  the  rubbish  lies  concealed  in  the 
middle,  KK.  In  the  bottom  there  are  six  courses  of  larger  bricks  ;  then 
some  less,  at  the  height  of  three  feet  ;  then  the  walls  are  bound  again 
with  three  courses  of  larger  bricks  ;  an  example  of  this  kind  still  re- 
mains in  the  Pantheon,  and  in  the  hot-baths  built  by  Diocletian. 

The  seventh  kind,  fig.  7  is  net-work  L.L  :  which  Palladio  did  not 
approve  of,  and  to  ensure  the  strength  ofwhich,  he  proposed  to  erect 
buttresses  at  the  angles  M.M.  and  to  place  transversely,  or  length- 
wise, six  courses  of  bricks  at  the  bottom  N.N.  and  in  the  middle  three 
.courses  O.O.  whenever  the  net  work  is  raised  six  feet. 

The  existing  examples  of  Roman  emplecton,  with  partial  cores  of 
jrubble-work,  or  brick,  sufficiently  prove  its  durability  ;  but  that  of 
the  Greeks  was  worked  throughout  the  whole  thickness  of  the  wall, 
in  the  same  manner  as  the  facing  of  the  fronts,  as  their  temples  now 
existing  testify. 

The  thickness  of  walls  should  be  regulated  according  to  the  na- 
ture of  the  materials,  and  the  magnitude  of  the  edifice.  Walls  of 
stone  may  be  made  one  fifth  thinner  than  those  of  brick  ;  and  brick- 


SI. 


Fu,.  1. 


Iitf.  7. 


Tio.  13. 


Fn,.  4. 


11       11  II 


m,.  5. 


j'Y.j.  <y. 


i  i  i  i  i 


l'?, i.  14. 


Ma.  3. 


Fla.  10 


rz 


A/  7.  //. 


J  L 


62.Sc. 


ON  BRICKLAYING. 


131 


walls,  in  the  basement  and  ground  stories  of  buildings  of  the  first 
rate,  should  be  reticulated  with  stones,  to  prevent  their  splitting  ;  a 
circumstance  which  has  been  two  much  disregarded  by  our  builders. 


SECTION  II.  Construction  of  Brick  Arches. 

Plate  XXXVI,  fig.  1 ,  represents  a  straight  arch  or  aperture  in  a  brick 
wall.  Describe  an  isosceles  triangle  on  CD.  the  width  of  the  arch 
as  a  base  line  whose  vertex  will  be  at  a,  produce  a  C.  to  E.  and  a 
D  to  F.  and  EF  will  be  extrados,  and  CD  the  intrados  of  the  arch. 

Divide  CD,  and  EF  in  to  the  same  number  of  equal  parts,  and 
make  the  bricks  to  correspond  with  these  parts. 

Fig.  2  is  a  segment  arch.  Describe  an  isosceles  triangle  as  in  fig  1. 
and  bisect  CD.  in  b.;  from  the  point  a,  with  the  radius  a  D  describe 
the  arc  DbC.  and  with  the  radius  a  C  produced  from  the  point  a  de- 
scribe the  extrados  and  C  b  D ,  will  be  the  intrados  of  the  arch. 

Fig.  3  is  a  semicircular  arch  ;  the  intrados  of  which  is  easily  found 
by  making  the  semidiameter  or  h  the  width  of  the  arch,  the  radius  of 
the  semicircle  b  eD. 

Fig.  4  is  a  semileptical  arch,  formed  from  three  points.  Divide 
Dd  the  width  of  the  arch  into  three  equal  parts  at  the  points  B.\. 
from  the  centre  A  of  Dd  erect  the  perpendicular  Ae,  and  produce  Ae 
at  pleasure  join  Ba,  making  Ba  equal  to  AD  ;  produce  aB  to  c,  at  the 
point  B,  with  the  radius  Be  ;  describe  the  arc  ed  ;  join  ba,  and  produce 
ba.  to  C.  then  with  the  radius  ac  at  the  point  a,  describe  the  arc 
c  e  C,  and  at  the  point  b  with  the  radius  bd  describe  the  arc  C  d  and 
the  D,  e  d.  the  intrados  of  the  intended  arch  will  be  complete. 

Figs.  5  and  6  show  the  construction  of  Gothic  arches  on  the  prin- 
ciples laid  down  in  the  Plate  S3,  fig.  1  and  3. 

Nos.  I  and  2  represent  the  application  of  inverted  arches  to  the 
foundations  of  brick  wall.    See  foundations. 


SECTION  III.  Bricklaying. 

Bricklaying  is  the  art  of  building  with  bricks,  or  the  uniting 
them,  by  cement  or  mortar,  into  various  forms  for  particular 
purposes. 

Bricks  are  laid  in  a  varied,  but  regular,  form  of  connection,  or 
bond,  as  exhibited  in  Plates  37  and  38.  The  mode  of  laying  them 
for  an  8  inch  walling,  shown  in  fig.  1  being  denominated  English, 
bond ;  and  fig.  2  Flemish  bond.  Fig.  3  is  English  bond,  in  a 
brick  and  a  half,  or  12  inch  walling  ;  and  fig.  4,  Flemish  Bond,  in 
the  same.  Fig.  5  represents  another  method  of  disposing  flemish 
bond  in  a  12  inch  wall.  Fig.  6  English  bond  in  a  16  inch,  or  a  two 
brick  thick  wall  ;  and  fig.  7,  English  bond,  in  a  two  and  a  half  brick 
thick  wall. 


132  OPERATIVE  MASONRY. 

Fig.  8  is  another  Brick  bond,  which  is  admired  for  its  regularity 
and  strength,  it  is  formed  of  brick  and  tiles,  and  connected  with  this 
Jig.  is  the  next  course  above  the  tiles,  composed  of  headers. 

Figs.  9,  10,  11,  12,  represent  square  courses,  inpairs  of  Flemish 
bond.  In  each  pair,  if  one  be  the  lower  course,  the  other  will  be  the 
upper  course. 

The  bricks  having  their  lengths  in  the  thickness  of  the  wall,  are 
termed  headers,  and  those  which  have  their  lengths  in  the  length  of 
the  wall  are  stretchers.  By  a  course ,  in  walling,  is  meant  the  bricks 
contained  between  two  planes  parallel  to  the  horizon,  and  termina- 
ted by  the  faces  of  the  wall.  The  thickness  is  that  of  one  brick  with 
mortar.  The  mass  formed  by  bricks  laid  in  concentric  order,  for 
arches  or  vaults,  is  also  denominated  a  course. 

The  disposition  of  bricks  in  a  wall,  of  which  every  alternate  course 
consist  of  headers,  and  of  which  every  course  between  every  two  near- 
est courses  of  headers  consist  of  stretchers,  constitutes  English  bond. 

The  disposition  of  bricks  in  a  wall  (except  at  the  quoins)  of  which 
every  alternate  brick  in  the  same  course  is  a  header,  and  of  which 
every  brick  between  every  two  nearest  header  is  a  stretcher,  consti- 
tutes Flemish  bond. 

It  is,  therefore,  to  be  understood  that  English  bond  is  a  continua- 
tion of  one  kind  throughout,  in  the  same  course  or  horizontal  layer, 
and  consists  of  alternate  layers  of  headers  and  stretchers,  as  shown  in 
the  plate  ;  the  headers  serving  to  bind  the  wall  together  in  a  longitu- 
dinal direction,  or  lengthwise,  and  the  stretchers  to  prevent  the  wall 
splitting  crosswise,  or  in  a  transverse  direction.  Of  these  evils  the 
first  is  of  the  worst  kind,  and  therefore  the  most  to  be  feared. 

It  is  supposed,  that  the  old  English  mode  of  brick-work  affords 
the  best  security  against  such  accidents  ;  as  work  of  this  kind, 
wheresoever  it  is  so  much  undermined  as  to  cause  a  fracture,  is  not 
subject  to  such  accidents,  but  separates,  if  at  all,  by  breaking  through 
the  solid  brick,  just  as  if  the  wall  were  composed  of  one  piece. 

The  ancient  brick-work  of  the  Romans  was  of  this  kind  of  bond, 
but  the  existing  specimens  are  very  thick,  and  have  three,  or  some- 
times more  courses  of  brick  laid  at  certain  intervals  of  the  height, 
stretchers  on  stretchers,  and  headers  on  headers,  opposite  the  return 
wall,  and  sometimes  at  certain  distances  in  the  length,  forming 
piers,  that  bind  the  wall  together  in  a  transverse  direction  ;  the  in- 
tervals between  these  piers  were  filled  up,  and  formed  panels  of  rub- 
ble or  reticulated  work  ;  consequently  great  substance,  with  strength, 
were  economically  obtained. 

It  will,  also,  be  understood  Flemish  bond  consists  in  placing,  in 
the  same  course,  alternate  headers  and  stretchers,  a  disposition  con- 
sidered as  decidedly  inferior  in  every  thing  but  appearance,  and 
even  in  this,  the  difference  is  trifling ;  yet,  to  obtain  it,  strength  is 
sacrificed,  and  bricks  of  two  qualities  are  fabricated  for  the  pur- 
pose ;  a  firm  brick  often  rubbed,  and  laid  in  what  the  workmen 
term  a  putty-joint  for  the  exterior,  and  an  inferior  brick  for  the  in- 
terior, substance  of  the  wall ;  but,  as  these  did  not  correspond  in 
thickness,  the  exterior  and  interior  surface  of  the  wall  would  not 
be  otherwise  connected  together  than  by  an  outside  heading  brick, 


ON  BRICKLAYING. 


133 


here  and  there  continued  of  its  whole  length  ;  but,  as  the  work 
does  not  admit  of  this  at  all  times,  from  the  want  of  agreement  in 
the  exterior  and  interior  courses,  these  headers  can  be  introduced 
only  where  such  a  correspondence  takes  place,  which,  sometimes, 
may  not  occur  for  a  considerable  space. 

Walls  of  this  kind  consist  of  two  faces  of  four  inch  work,  with 
very  little  to  connect  them  together,  and  what  is  still  worse  the 
interior  face  often  consists  of  bad  brick,  little  better  than  rubbish. 
The  practice  of  Flemish  bond  has,  notwithstanding,  continued  in 
England,  from  the  time  of  William  and  Mary,  when  it  was  intro- 
duced, with  many  other  Dutch  fashions,  and  the  workmen  are  so 
infatuated  with  it,  that  there  is  now  scarcely  an  instance  of  the  old 
English  bond  to  be  seen. 

The  frequent  splitting  of  walls  into  two  thicknesses  has  been  at- 
tributed to  the  Flemish  bond  alone,  and  various  methods  have  been 
adopted  for  its  prevention.  Some  have  laid  laths  or  slips  of  hoop 
iron,  occasionally,  in  the  horizontal  points  between  the  two  courses; 
others  have  laid  diagonal  courses  of  bricks  at  certain  heights  from 
each  other  ;  but  the  effect  of  the  last  method  is  questionable,  as  in 
the  diagonal  course,  by  their  not  being  continued  to  the  outside,  the 
bricks  are  much  broken  where  the  strength  is  required. 

Other  methods  of  uniting  complete  bond  with  Flemish  facings 
have  been  described,  but  they  have  been  found  equally  unsuccessful. 
In^o-s.  3  and  4  Plate  38  the  interior  bricks  are  represented  as  disposed 
with  intention  to  unite  these  two  particulars  ;  the  Flemish  facings 
being  on  one  side  of  the  wall  only  ;  but  this,  at  least,  falls  short  of 
the  strength  obtained  by  English  bond.  Another  evil  attending  this 
disposition  of  the  bricks  is,  the  difficulty  of  its  execution,  as  the  ad- 
justment of  the  bricks  in  one  course  must  depend  on  the  course  be- 
neath, which  must  be  seen  or  recollected  by  the  workman  ;  the  first 
is  difficult  from  the  joints  of  the  under  course  being  covered  with 
mortar,  to  bed  the  bricks  of  the  succeeding  course  ;  and  for  the  work- 
man to  carry  in  his  mind  the  arrangement  of  the  preceding  course 
can  hardly  be  expected  from  him  ;  yet,  unless  it  be  attended  to,  the 
joints  will  be  frequently  brought  to  correspond,  dividing  the  wall 
into  several  thicknesses,  and  rendering  it  subject  to  splitting,  or  sep- 
aration. But,  in  the  English  bond,  the  outside  of  the  last  course 
points  out  how  the  next  is  to  be  laid  so  that  the  workman  cannot 
mistake. 

The  outer  appearance  is  all  that  can  be  urged  in  favour  of  Flem- 
ish bond,  and  many  are  of  opinion,  that,  were  the  English  mode  ex- 
ecuted with  the  same  attention  and  neatness  that  is  bestowed  on  the 
Flemish,  it  would  be  considered  as  equally  handsome  ;  and  its  adop- 
tion, in  preference,  has  been  strenuously  recommended. 

In  forming  English  bond,  the  following  rules  are  to  be  observed. 

1st.  Each  course  is  to  be  formed  of  headers  and  stretchers  alter- 
nately, asyig*.  1. 

2d.  Every  brick  in  the  same  course  must  be  laid  in  the  same 
direction  ;  but  in  no  instance,  is  a  brick  to  be  placed  with  its  whole 
length  along  the  side  of  another  ;  but  to  be  so  situated  that  the  end 
of  one  may  reach  to  the  middle  of  the  others  which  lie  contiguous 


134 


OPERATIVE  MASONRY. 


to  it,  excepting  the  outside  of  the  stretching-course,  where  three* 
quarter  bricks  necessarily  occur  at  the  ends,  to  prevent  a  continual 
upright  joint  in  the  face-work. 

3d.  A  wall,  which  crosses  at  a  right-angle  with  another,  will 
have  all  the  bricks,  of  the  same  level  course  in  the  same  parallel  di- 
rection, which  completely  binds  the  angles,  as  shown  by  Jigs.  1,  3, 
and  6.  Plate  XXX?  II. 

The  great  principle  in  the  practice  of  brick-work  lies  in  the  proclivity 
or  certain  motion  of  absolute  gravity,  caused  by  a  quantity,  or  mul- 
tiplicity of  substances  being  added  or  fixed  in  resistible  matter, 
and  which,  therefore,  naturally  tends  downwards,  according  to  the 
weight  and  power  impressed.  In  bricklaying,  this  proclivity,  chiefly 
by  the  yielding  mixture  of  the  matter  of  which  mortar  is  composed, 
cannot  be  exactly  calculated  ;  because  the  weight  of  a  brick,  or  any 
other  substances  laid  in  mortar,  will  naturally  decline  according  to 
its  substance  or  quality  ;  particular  care  should  be  taken,  therefore, 
that  the  material  be  of  one  regular  and  equal  quality  all  through  the 
building  ;  and  likewise,  that  the  same  force  should  be  used  to  one 
brick  as  to  another  ;  that  is  to  say,  the  stroke  of  the  trowel,  a  thing 
or  point  in  practice  of  much  more  consequence  than  is  generally 
imagined  ;  for  if  a  brick  be  actuated  by  a  blow,  this  will  be  a  much 
greater  pressure  upon  it  than  the  weight  of  twenty  bricks.  It  is, 
also,  especially  to  be  remarked,  that  the  many  bad  effects  arising 
from  mortar  not  being  of  a  proper  quality  should  make  masters 
very  cautious  in  the  preparation  of  it,  as  well  as  the  certain  quality 
of  materials  of  which  it  is  composed,  so  that  the  whole  structure 
may  be  of  equal  density,  as  nearly  as  can  be  effected. 

Here  we  may  notice  a  particular  which  often  causes  a  bulging  in 
large  flank  walls,  especially  when  they  are  not  properly  set  oft'  on 
both  sides  ;  that  is,  the  irregular  method  of  laying  bricks  too  high 
on  the  front  edge  ;  this,  and  building  the  walls  too  high  on  one  side, 
without  continuing  the  other,  often  causes  defects.  Notwithstanding, 
of  the  two  evils,  this  is  the  least  ;  and  bricks  should  incline  rather 
to  the  middle  of  the  wall,  that  one  half  of  the  wall  may  act  as  a 
shore  to  the  other.  But  even  this  method,  carried  too  far,  will  be 
more  injurious  than  beneficial,  because  the  full  width  of  the  wall, 
in  this  case,  does  not  take  its  absolute  weight,  and  the  gravity  is  re- 
moved from  its  first  line  of  direction,  which,  in  all  walls,  should 
be  perpendicular  and  united  ;  and  it  is  farther  to  be  considered 
that,  as  the  walls  will  have  a  superincumbent  weight  to  bear,  ade- 
quate to  their  full  strength,  a  disjunctive  digression  is  made  from  the 
right  line  of  direction  ;  the  conjunctive  strength  becomes  divided  ; 
and  instead  of  the  whole  or  united  support  from  the  wall,  its  strength 
is  separated  in  the  middle,  and  takes  two  lateral  bearings  of  gravity  ; 
each  insufficient  for  the  purpose  ;  therefore,  like  a  man  overloaded 
either  upon  his  head  or  shoulders,  naturally  bends  and  stoops  to  the 
force  impressed  ;  in  which  mutable  state  the  grievances  above  no- 
ticed, usually  occur. 

Another  great  defect  is  frequently  seen  in  the  fronts  of  houses,  in 
some  of  the  principal  ornaments  of  brick-work,  as  arches  over  win- 
dows, &c,  and  which  is  too  often  caused  by  a  want  of  experience  in 


OF  FOUNDATIONS. 


135 


rubbing  the  bricks  ;  which  is  the  most  difficult  part  of  the  branch, 
and  ought  to  be  very  well  considered.  The  faults  alluded  to  are 
the  bulging  or  convexity  in  which  the  faces  of  arches  are  often 
found,  after  the  houses  are  finished,  and  sometimes  loose  in  the  key 
or  centre  bond.  The  first  of  these  defects,  which  appears  to  be 
caused  by  too  much  weight,  is,  in  reality,  no  more  than  a  fault  in 
the  practice  of  rubbing  the  bricks  too  much  off  on  the  insides  ;  for 
it  should  be  a  standing  maxim,  (if  you  expect  them  to  appear  straight 
under  their  proper  weight,)  to  make  them  the  exact  gauge  on  the 
inside  that  they  bear  upon  the  front  edges;  by  whkh  means  their 
geometrical  bearings  are  united,  and  tend  to  one  centre  of  gravity. 

The  latter  observation,  of  camber  arches  not  being  skewed  enough, 
is  an  egregious  iault  ;  because  it  takes  greatly  from  the  beauty  of  the 
arch,  and  renders  it  insignificant.  The  proper  method  of  skewing 
all  camber  arches  should  be  one  third  of  their  height.  For  instance, 
if  an  arch  is  nine  inches  high,  it  should  skew  three  inches  ;  one  of 
twelve  inches,  four  ;  one  of  fifteen,  five  ;  and  so  of  all  the  numbers 
between  those.  Observe,  in  dividing  the  arch,  that  the  quantity  con- 
sists of  an  odd  number  ;  by  so  doing,  you  will  have  proper  bond  ; 
and  the  key  bond  in  the  middle  of  the  arches  ;  in  which  state  it 
must  always  be,  both  for  strength  and  beauty.  Likewise  observe, 
that  arches  are  drawn  from  one  centre  ;  the  real  point  of  camber 
arches  is  obtained  from  the  above  proportion.  First,  divide  the 
height  of  the  arch  into  three  parts  ;  one  is  the  dimension  for  the 
skewing  ;  a  line  drawn  from  that  through  the  point  at  the  bottom 
to  the  perpendicular  of  the  middle  arch,  gives  the  centre ;  to  which 
all  the  rest  must  be  drawn. 


SECTION  IV.— Foundations. 
RULES  TO  BE  OBSERVED  IN  LAYING  FOUNDATIONS. 

If  a  projected  building  is  to  have  cellars,  under-ground  kitchens, 
&c.  there  will  commonly  be  found  a  sufficient  bottom,  without  any 
extra  process,  for  a  good  solid  foundation.  When  this  is  not  the 
case,  the  remedies  are  to  dig  deeper;  or  to  drive  in  large  stones  with 
the  rammer  ;  or  by  laying  in  thick  pieces  of  oak,  crossing  the  direc- 
tion of  the  wall,  and  planks  of  the  same  timber,  wider  than  the  in- 
tended wall  and  running  in  the  same  direction  with  it.  The  last 
one  to  be  spiked  firmly  to  the  cross-pieces  to  prevent  their  sliding, 
the  ground  having  been  previously  well  rammed  under  them. 

The  mode  of  ascertaining  if  the  ground  be  solid  is  by  the  rammer  ; 
if  by  striking  the  ground  with  this  tool,  it  shake,  it  must  be  pierced 
with  a  borer,  such  as  is  used  by  well-diggers  ;  and  having  found 
how  deep  the  firm  ground  is  below  the  surface,  you  must  proceed 
to  remove  the  loose  or  soft  part,  taking  care  to  leave  it  in  the  form 
of  steps  if  it  be  tapering,  that  the  stones  may  have  a  solid  bearing, 
and  not  be  subject  to  slide,  which  would  be  likely  to  happen  if  the 
ground  were  dug  in  the  form  of  an  inclined  plane. 

If  the  ground  prove  variable,  and  be  hard  and  soft  at  different 
18 


136 


OPERATIVE  MASONRY. 


places,  the  best  way  is  to  turn  arches  from  one  hard  spot  to  another* 
Inverted  arches  have  been  used  for  this  purpose  with  great  success, 
by  bringing  up  the  piers,  which  carry  the  principal  weight  of  the 
building,  to  the  intended  height  and  thickness,  and  then  turning  re- 
versed arches  from  one  pier  to  another,  as  shown  in  Jigs.  5  and  6, 
plate  XXXVI,  Nos.  1  and  2. 

In  this  case,  it  is  clear  that  the  piers  cannot  sink  without  carrying 
the  arches,  and  consequently,  the  ground  on  which  they  lie,  with 
them.  This  practice  is  excellent  in  such  cases,  and  should  there- 
fore be  general,  wherever  required. 

Where  the  hard  ground  is  to  be  found  under  the  apertures  only, 
build  your  piers  on  those  places,  and  turn  arches  from  one  to  the 
other.  In  the  construction  of  arches  some  attention  must  be  paid  to 
the  breadth  of  the  insisting  pier,  whether  it  will  cover  the  arch  or 
not ;  for,  suppose  the  middle  of  the  piers  to  rest  over  the  middle  of 
the  summit  of  the  arches,  then  the  narrower  the  piers,  the  more 
curvature  the  supporting  arch  ought  to  have  at  the  apex.  When 
arches  of  suspension  are  used,  the  intrados  ought  to  be  clear,  so 
that  the  arch  may  have  the  full  effect  ;  but,  as  already  noticed,  it 
will  also  be  requisite  here  that  the  ground  on  which  the  piers  are 
erected  be  uniformly  hard  ;  for  it  is  better  that  it  should  be  uniform, 
though  not  so  hard  as  might  be  wished,  then  to  have  it  unequally 
so  ;  because  in  the  first  case,  the  piers  would  descend  uniformly,  and 
the  building  remain  uninjured  ;  but  in  the  second,  a  vertical  frac- 
ture would  take  place,  and  endanger  the  whole  structure. 


SECTION  V.— Walls,  &c. 

The  foundation  being  properly  prepared,  the  choice  of  materials 
is  to  be  considered.  In  places  much  exposed  to  the  weather,  the 
hardest  and  best  bricks  must  be  used,  and  the  softer  reserved  for  in- 
door work,  or  for  situations  less  exposed. 

If  laying  bricks  in  dry  weather,  and  the  work  is  required  to  be 
firm,  wet  your  bricks  by  dipping  them  in  water,  or  by  causing  wa- 
ter to  be  thrown  over  them  before  they  are  used.  Few  workmen 
are  sufficiently  aware  of  the  advantage  of  wetting  bricks  ;  but  ex- 
perience has  shown,  that  works  in  which  this  practice  has  been  fol- 
lowed, have  been  much  stronger  than  others,  wherein  it  has  been 
neglected.  It  is  particularly  serviceable,  where  work  is  carried  up 
thin,  and  putting  in  grates,  furnaces,  &c. 

In  the  winter  season,  so  soon  as  frosty  and  stormy  weather  set  in, 
cover  your  wall  with  straw  or  boards  ;  the  first  is  the  best,  if  well 
secured,  as  it  protects  the  top  of  the  wall,  in  some  measure,  from 
frost,  which  is  very  prejudicial,  particularly  when  it  succeeds  much 
rain  ;  for  the  rain  penetrates  to  the  heart  of  the  wall,  and  the  frost, 
by  converting  the  water  into  ice,  expands  it,  and  causes  the  mortar 
to  assume  a  short  and  crumbly  nature,  and  altogether  destroys  its 
tenacity. 

In  working  up  a  wall,  it  is  proper  not  to  work  more  than  four  or 
five  feet  at  a  time  ;  for,  as  all  walls  shrink  immediately  after  build- 


WALLS,  &c. 


187 


incr  the  part  which  is  first  brought  up  will  remain  stationary  ;  and 
when  the  adjoining  part  is  raised  to  the  same  height,  a  shrinking  or 
setling  will  take  place,  and  separate  the  former  from  the  latter,  caus- 
ing a  crack,  which  will  become  more  and  more  evident,  as  the  work 
proceeds. 

In  carrying  up  any  particular  part,  each  side  should  be  sloped  off, 
to  receive  the  bond  of  the  adjoining  work  on  the  right  and  left. 
Nothing  but  absolute  necessity  can  justify  carrying  the  work  higher 
in  any  particular  part,  than  one  scaffold  ;  for,  wherever  it  is  so  done, 
the  workmen  should  be  answerable  for  all  the  evil  that  may  arise 
from  it. 

The  distinctions  of  Bond  have  already  been  shown,  and  we  shall 
now  detail  them  more  particularly  ;  refer ing  to  Plate  XXXVII,  in 
which  the  arrangement  of  bricks  of  different  thickness,  so  as  to  form 
English  Bond,  is  shown  in  figs.  1,  3,  6,  and  7. 

The  bond  of  a  wall  8  inches  is  represented  by  fig.  I.  In  order  to 
prevent  two  upright  or  vertical  joints  from  running  over  each  other, 
at  the  end  of  the  first  stretcher  from  the  corner,  place  the  return- 
stretcher,  which  is  a  header,  in  the  face  that  the  stretcher  is  in  be- 
low, and  occupying  half  its  length  ;  a  quarter  brick  is  placed  on  its 
side,  forming  together  6  inches,  and  leave  a  lap  2  inches  for  the 
next  header,  which  lies  with  its  middle  upon  the  middle  of  the 
header  below,  and  forms  a  continuation  of  the  bond.  The  three- 
quarter  brick,  or  brick-bat,  is  called  a  closer. 

Another  way  of  effecting  this,  is  by  laying  a  three-quarter  bat 
at  the  corner  of  the  stretching  course  ;  for,  when  the  corner  head 
comes  to  be  laid  over  it,  a  lap  of  2  inches  will  be  left  at  the  end  of 
the  stretchers  below  for  the  next  header  ;  which,  when  laid,  its 
middle  will  come  over  the  joint  below  the  stretcher,  and  in  this 
manner  form  the  bond. 

In  a  12  inch,  or  brick-and-half  wall,  (fig.  3,)  the  stretching  course 
upon  one  side,  is  so  laid  that  the  middle  of  the  breadth  of  the 
bricks,  upon  the  opposite  side,  falls  alternately  upon  the  middle  of 
the  stretchers  and  upon  the  points  between  the  stretchers. 

In  a  two-brick  wall,  (fig.  6.)  every  alternate  header,  in  the  heading 
course,  is  only  half  a  brick  thick  on  both  sides,  which  breaks  the 
the  joints  in  the  core  of  the  wall. 

In  a  two-brick  and  a  half  wall,  (fig.  7,)  the  bricks  are  laid  as 
shown  in  fig.  6. 

Flemish  bond,  for  an  eight  inch  wall,  is  represented  in  fig.  2, 
wherein  two  stretchers  lie  between  two  headers,  the  length  of  the 
headers  and  the  breadth  of  the  stretchers  extending  the  whole  thick- 
ness of  the  wall. 

In  a  brick-and-half  Flemish  bond,  (fig.  4,)  one  side  being  laid  as 
in  fig.  2,  and  the  opposite  side,  with  a  half-header,  opposite  to  the 
middle  of  the  stretcher,  and  the  middle  of  the  stretcher  opposite 
the  middle  of  the  end  of  the  header. 

Figure  5,  exhibits  another  arrangement  of  Flemish  bond,  wherein 
the  bricks  are  disposed  alike  on  both  sides  of  the  wall,  the  tail  of 
the  headers  being  placed  contiguous  to  each  other,  so  as  to  form 
square  spaces  in  the  core  of  the  wall  for  hajf-bricks. 


138 


OPERATIVE  MASONRY. 


The  face  of  an  upright  wall,  English  bond,  is  represented  by  fig, 
13  and  that  of  Flemish  bond,  by  fig.  14. 


SECTION  VI. 

THE   CONSTRUCTION   OF  CHIMNIES. 

Many  able  and  scientific  men  have  treated  on  this  subject,  but  the 
result  of  their  observations  serve  only  to  prove,  what  is  the  object 
of  every  day's  experience,  namely,  that  rarefied  air  is  lighter  and 
less  dense  than  cold  air  ;  and  that  it  will  ascend  with  a  velocity 
proportionate  to  its  rarefaction,  unless  obstructed  by  other  bodies. 

Heat,  that  is  generated  by  the  combustion  of  fuel,  exists  under 
two  distinct  forms  ;  and  is  known  by  the  names  of  combustible  and 
radiant  heat.  Combustible  heat  partakes  of  smoke,  and  is  carried 
off  with  it  into  the  upper  regions  ;  while  radiant  heat  is  communi- 
cated to  opposing  bodies  in  contact  with  its  rays. 

It  is  stated  by  some  that  combustible  heat  combined  with  air  and 
smoke  exists  in  the  proportion  of  four  to  one,  compared  to  radiant 
heat  ;  but  its  correct  proportion  has,  perhaps,  never  been  ascer- 
tained. 

It  is  however  certain,  that  very  little  radiant  heat  will  escape 
from  a  smothered  combustion,  while  a  dense  smoke  will  very  slowly 
ascend,  and  sometimes  a  portion  of  it  is  discharged  into  the  room, 
and  the  chimney  is  pronounced  smoky,  while  the  epithets  uttered 
against  masons,  on  such  occasions,  would  be  more  properly  applied 
to  the  builders  of  the  fire. 

As  nature  acts  by  certain  laws,  we  may  derive  more  profitable  in- 
formation by  a  proper  observance  of  them,  than  from  accidental 
occurrences. 

It  is  one  of  the  laws  of  nature,  that  rarefied  air  ascends,  while 
cold  or  dense  air  descends.  On  the  same  principle  water  discharges 
itself  most  copiously  through  a  channel  of  an  uniform  and  direct 
surface,  on  the  same  inclination.  Therefore,  channels,  that  are  ob- 
structed by  eddies,  and  the  discharge  of  other  streams  into  them, 
are  impeded,  and  the  velocity  of  the  water  diminished,  so  as  often 
to  produce  what  is  called  back-water  for  a  considerable  distance, 
which,  when  removed,  permits  the  water  to  flow  with  rapidity. 
Short  bends  and  turnings  also  present  obstacles  to  the  current  or 
flow  of  water,  by  which  whirlpools  are  often  seen  in  actual  contact 
with  the  natural  stream.  The  same  observations  may  be  applied  to 
rarefied  air  or  smoke.  Hence  those  flues  will  carry  smoke  the  best 
which  arise  perpendicularly  in  an  uniform  direction. 

Angles  and  turnings  present  obstacles  to  the  progress  of  the  smoke, 
and  should  be  avoided  as  much  as  possible. 

Particular  attention  should  be  paid  to  the  formation  of  the  throat 
of  the  chimney.  The  dimensions  of  which  should  in  no  case  ex- 
ceed the  number  of  square  inches  contained  in  a  horizontal  section 
of  the  flue.    It  has  been  (Contended  by  some  that  it  should  be  smaller 


FIRE-PLACES. 


139 


than  this,  while  others  have  thought  that  it  should  he  larger  ;  but  ex- 
perience has  shown  both  of  these  opinions  to  be  erroneous.  When 
the  throat  is  smaller,  the  frequent  rushes  of  cold  air  into  it,  from 
the  opening  of  doors,  &c.  sends  a  gush  of  smoke  into  the  room,  by 
obstructing  the  upward  current  of  rarefied  air. 

When  the  throats  are  larger,  eddies  are  formed  in  them,  and  the 
smoke,  becoming  dense  by  the  steam  of  the  fuel,  choaks  the  flue, 
and  instead  of  ascending,  is  puffed  into  the  room. 

Experience  has  shown  the  best  construction  to  be  that,  where  the 
throat  contains  as  many  square  inches  as  a  section  of  the  flue.  If 
the  latter,  for  instance,  is  144  inches,  the  throat  should  be  4  feet  long  ; 
and  3  inches  wide  nearly  on  a  level  with  the  mantle-bar,  or  at  the 
top  of  the  opening  of  the  fire-place,  and  graduated  to  the  regular 
dimensions  of  the  flue. 

As  represented  in  Plate  XXXIX,  Jigs.  3  and  4.  In  this  Plate,  Jig.  3  shows  a 
side  perpendicular  section  of  a  chimney  ;  c?,the  partition  wall ;  a,  the  throat;  b,  the 
breast ;  c,  the  height  of  the  graduation  to  form  the  regular  flue ;  E,  the  depth  of 
the  jamb ;  f,  a  trimmer  to  support  the  hearth  in  form  of  a  segment  arch. 

Fig.  4  is  the  front  elevation  of  Jig.  3,  representing  the  flues,  fire-places,  a  hor- 
izontal section  at  the  hearths,  as  DE  ;  a  section  of  the  flues  at  the  side  of  the 
fire-places  I ;  the  core  of  the  chimney,  H  ;  the  jambs  F  ;  the  back  of  the  fire- 
places G,  with  the  inclined  part  of  the  back. 

FIRE-PLACES. 

In  the  selection  of  materials  for  the  construction  of  fire-places, 
those  should  be  preferred,  which  contain  the  least  metallic  ingredi- 
ents.. Metals  are  absorbents  of  heat,  and  consequently  occasion  less 
heat  to  be  radiated  into  the  room,  than  materials  of  a  different  na- 
ture. Soapstone  has  been  found  to  be  one  of  the  best  materials  for 
this  purpose.  It  contains  but  little  metallic  substance  compared  to 
brick  ;  it  is  capable  of  a  high  degree  of  polish  and  of  being 
easily  kept  clean,  by  which  means  the  rays  of  heat  are  reflected  into 
the  room. 

The  proportions  of  a  fire-place  should  in  some  degree  be  regula- 
ted according  to  the  size  of  the  room,  for  which  it  is  intended  to 
warm. 

If  the  room  is  18  feet  in  length,  a  fire-place  of  4  feet  3  inches  in 
width,  from  jamb  to  jamb  ;  and  3  feet  in  height  where  the  room  is 
12  feet  in  the  same  direction,  or  1-4  of  the  height  of  the  room,  may, 
in  general,  be  considered  of  suitable  proportions.  The  jambs  should 
form  an  angle  of  135  degrees  with  the  back.  See  PlateXXXIX,  fig,  4, 
H  the  jamb,  the  back  edge  of  which  should  be  rabbited  and  fitted 
to  a  groove  in  the  back  to  keep  it  in  its  place,  F  should  be  set 
plumb  about  2-5ths  of  the  height  of  the  back  FG  ;  G  should  be  in- 
clined forward  to  within  7  inches  of  the  front  line,  allowing  4 
inches  for  the  thickness  of  the  breast,  and  3  inches  will  remain  for 
the  passage  of  the  smoke. 

The  communication  of  hot  air  to  rooms.  This  subject  is  worthy 
of  attention,  in  as  much  as  the  temperature  of  bed  chambers  may 


*       »     o  •    o  • 

•  J  ,•>>••• 

.  -  ...  •  ' 


140 


OPERATIVE  MASONRY. 


be  regulated  by  it,  as  well  as  the  danger  of  fire,  and  the  destructive 
and  fatal  effects  of  charcoal  diminished.  This  improvement  may 
be  adapted  to  common  fire-places  as  well  as  to  grates,  and  the  hot 
air  carried  from  the  first  to  the  upper  stories. 

A  little  below  the  hearth  in  the  first  story,  a  small  aperture  is 
opened,  of  about  2  inches  square,  through  which  to  receive  fresh 
air  from  the  outside  of  the  house  into  a  cavity,  as  large  as  can  with 
convenience  be  made  between  the  jambs  and  the  brick,  which  form 
the  wall  of  the  chimney,  this  cavity  should  be  made  tight,  with  an 
aperture  for  the  insertion  of  tubes  of  copper  or  tin,  which  are  to  be 
inserted  in  the  aperture  with  stops  or  slides  to  regulate  the  quantity 
of  air  to  be  admitted  into  the  room.  The  air  enters  about  two  feet 
from  the  floor.  By  turning  the  slide,  the  air  is  made  to  ascend  into 
other  apartments  at  pleasure. 

Plate  XXXIX,  jig.  4,  L,  is  the  generator  of  rarefied  air ;  o  the  tube  with  a  slide 
at  k ;  the  ascending  pipe  should  be  about  4  inches  square ;  m  shows  its  passage 
at  the  hearth. 

Chimney-pieces  are  of  various  forms,  as  the  fancy  or  taste  of  the  proprietor 
may  dictate. 

In  Plate  XL,^.  1,  isadoric  chimney-piece.  No.  1,  a  section  of  the  jambs, back 
facing,  flinth  and  pillars,  drawn  on  a  scale  of  1-2  inch  to  a  foot,  No.  2  the  shelf. 
Fig.  2  represents  an  Ionic  chimney-piece  ;  No.  1  a  section  ;  No,  2  the  shelf;  the 
line  a  shows  a  projection  of  the  entablature  ;  6,  the  facing  under  the  entablature, 
drawn  on  a  scale  of  1-2  an  inch  to  a  foot. 


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